Methods For Improving Production In Gas Phase Polymerization

ABSTRACT

The present disclosure relates to processes for production of polyolefins from olefin monomer(s) in a gas phase reactor using condensing agent(s) (CAs), and in particular relates to controlling condensed phase cooling in a gas phase reactor used to polymerize olefin monomer(s). The method may include introducing first and second condensing agent(s) into the reactor at ratio(s) determined by ascertaining a stick limit for the first condensing agent, calculating an equivalence factor relating the first and second condensing agents, ascertaining total allowable condensing agent, and calculating amount of the first condensing agent removed and replaced by the second condensing agent. The method may further include calculating the dew point limit of a gas phase composition including olefin monomer(s) as well as the first and second condensing agents; and determining if introducing a mixture comprising the olefin monomer(s) and the condensing agent composition would exceed the calculated dew point limit.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application Ser.No. 62/821,746, filed Mar. 21, 2019 and entitled “Methods for ImprovingProduction in Gas Phase Polymerization,” the disclosure of which ishereby incorporated by reference in its entirety.

FIELD

The present disclosure relates to systems and methods for operating apolyolefin polymerization reactor within dew point constraints whileimproving production rates.

BACKGROUND

Polyolefins may be produced using gas phase polymerization processes. Ifthe process is a gas-phase fluidized bed polymerization process, theprocess may include a gas stream including one or more monomerscontinuously passed through a fluidized bed of catalyst and growingpolymer particles. As polymerization occurs, a portion of the monomersare consumed and the gas stream is heated in the reactor by the heat ofpolymerization. A portion of the gas stream exits the reactor and may berecycled back to the reactor with additional monomers and additives. Therecycle stream may be cooled, so as to maintain the temperature of theresin and gas phase composition inside the reactor below the upperstickiness temperature. A stickiness temperature is a temperature atwhich the reaction mixture including polymer particles begins to sticktogether forming agglomerates. Particle agglomerations may lead to theformation of chunks or sheets of polymer that cannot be removed from thereactor as product and which may fall onto the reactor distributor plateimpairing fluidization of the bed or causing reactor failure.Additionally, since the polymerization reaction is exothermic, theamount of polymer produced in a fluidized bed polymerization process maybe correlated to the amount of heat that can be withdrawn from thereaction zone.

There may be advantages to cool the recycle stream below its dew pointresulting in condensing a portion of the gaseous recycle stream outsideof the reactor. The dew point of the recycle stream is the temperatureat which liquid condensate first begins to form in the gaseous recyclestream. The dew point can be calculated knowing the gas composition andis thermodynamically defined using an equation of state. The process ofpurposefully condensing a portion of the recycle stream is referred toin the industry as “condensed mode” operation. When a recycle streamtemperature is lowered to a point below its dew point in condensed modeoperation, an increase in polymer production may be possible.

Cooling of the recycle stream to a temperature below the dew pointtemperature produces a two-phase gas/liquid mixture that may haveentrained solids contained in both phases. The liquid phase of thetwo-phase gas/liquid mixture in condensed mode operation is generallyentrained in the gas phase of the mixture. Vaporization of the liquidoccurs when heat is added or pressure is reduced. Generally, thevaporization occurs when the two-phase mixture enters the fluidized bed,with the heat of polymerization providing the heat of vaporization. Thevaporization thus provides an additional means of extracting heat ofreaction from the fluidized bed.

The cooling capacity of the recycle gas may be increased further whileat a given reaction temperature and a given temperature of the coolingheat transfer medium by adding non-polymerizing, non-reactive materialsto the reactor, which are condensable at the temperatures encountered inthe process heat exchanger (cooler). The non-reactive condensablematerials are collectively referred to as condensing agents (CAs),sometimes referred to as induced condensing agents because of the addedcooling they induce. Increasing concentrations of CAs in the reactorcauses corresponding increases in the dew point temperature of thereactor gas, which promotes higher levels of condensing, higher heattransfer (better cooling), and improved production rates from thereactor. However, the use of a CA is governed by its solubility in thepolymer, where the CA acts to depress the polymer melting point.Attempts to operate polymerization reactors with excessive CAconcentrations have led to the polymer particles suspended in the fluidbed to soften and become cohesive or “sticky” and, in some cases, tosolidification of the fluid bed in the form of large chunks or sheets.While the use of a CA may improve polymer production, there remains achallenge in balancing the increased cooling capacity against polymersoftening and stickiness.

Adding to the complexity of control of stickiness while using CAs, theaddition of CAs to the gas stream entering the reactor affects the dewpoint of the gas phase composition in the reactor. In many processes thereactor conditions are not near those that might cause issues with dewpoint of the gas phase composition within the reactor. Furthermore,without the addition of CAs, reactor conditions similarly do not nearthe dew point of the gas phase composition. However, the desire forincreased production has led to greater addition of CAs and use ofreactors that run at increased pressures, which in turn brings thereactor conditions and dew point of the gas phase composition closertogether.

At temperatures above, but near the dew point, a portion of the gasphase composition may undergo capillary condensation. Capillarycondensation may occur in a porous (or semi-porous) medium (e.g. formingpolymer resin), where the confined space may increase the number ofvapor interactions and cause condensation to begin at temperatures abovethe dew point of a gas phase composition. Because reactor shutdown maybe costly, and may be caused by capillary condensation, a lower limit onreactor temperature is set at some number of degrees above the actualdew point, which is referred to as the dew point limit (DPL). If thereactor is operated at a temperature below the DPL, a portion of thegases may condense and the resulting liquid may create a secondstickiness regime, in which the fluidized bed is compromised, which maylead to reactor failure. The temperature at or below the dew point limitis a lower stickiness temperature at which the reaction mixtureincluding polymer particles begins to stick together formingagglomerates. Therefore, the benefit of increased cooling capacityshould be balanced with the possibility of creating a gas phasecomposition, a portion of which condenses in the reactor and causespolymer stickiness. The typical course of action as reaction conditionsnear dew point limits is to reduce the quantity of CAs or vent thereactor gases causing a drop in reactor pressure.

Furthermore, different polymer products vary widely in their ability totolerate specific CAs, some having a relatively high tolerance(expressed in partial pressure of the CA in the reactor), e.g. 50 psia,while other polymers may tolerate as little as 5 psia. In polymers withlower tolerance, the heat transfer limited production rates undersimilar conditions are substantially lower. Polymers which possess amore uniform comonomer composition distribution may have a highertolerance to the partial pressure of the CA in the reactor. Typicalmetallocene catalysts are a good example of catalysts that may producepolymers having a more uniform comonomer composition. However, at somepoint even these metallocene produced polymers reach a limiting CAconcentration that induces stickiness.

At higher temperatures, the concentration of a CA which causes thepolymer particle to become sticky is referred to as the stick limit (SL)for that particular CA. At a given concentration of CA, a highertemperature that causes the polymer resin to become sticky is the upperstickiness temperature. Similarly, a lower temperature that causes thepolymer resin to become sticky is the lower stickiness temperature. TheDPL is a limit set to avoid the lower stickiness temperature, wherestickiness may be caused by condensation of a portion of the gas phasecomposition within the reactor. The temperature determines whetherincreased concentration of CA composition causes condensation of liquidfrom the gas phase composition (reaching the lower stickinesstemperature), or causes softening of the polymer resin with heat andincreased solubility of the gas phase composition (reaching the upperstickiness temperature). The upper stickiness temperature, the SL, thelower stickiness temperature, and the DPL depend on several factors inaddition to the polymer type, including reactor temperature, pressure,comonomer type, and comonomer concentration. Further, with the effect oftemperature, CA level, and comonomer levels all affecting the onset ofstickiness, determining the point at which stickiness begins to occurcan be challenging. Therefore, the concentration of a CA is maintainedbelow its SL and the temperature below the upper stickiness limit andabove the DPL, allowing the reactor to be maintained in a non-stickingregime below the upper stickiness temperature and above the DPL.

It may be possible to use a combination of CAs (a CA composition) toincrease condensed phase cooling (and therefore production rates) whileavoiding stickiness in the reactor. For the production of polyolefinsusing a CA composition, there is a need to balance the ratios of variousCAs to provide the maximum production rate while also avoidingstickiness within the reactor. Not using a method to balance the ratiosof CAs may cause a reactor to run at lower than optimal productionrates—which is an unfavorable economic operating condition. Worse, alack of methodology in balancing the composition of CAs could lead toreactor shutdown due to inadvertently running at a condition thatcreates stickiness. The upper and lower stickiness temperatures, and byassociation the DPL may vary with reactor conditions including pressureand composition of the gas stream entering the reactor. Because reactorconditions vary in real-time, the methods used to balance the ratios ofCAs should also operate in real-time.

Even within the constraints of safe operation, real-time control of gasphase polymerization reactors is complex. The complexity of reactorcontrol adds further to the difficulty and uncertainty ofexperimentation if one wishes to alter operating conditions to achievehigher production rates. Large-scale gas phase plants are expensive andhighly productive. Risks associated with experimentation in such plantsare high because downtime (such as that caused by passing the sticklimit) is costly. Therefore, exploring design and operating boundariesexperimentally is difficult in view of the costs and risks.

There is a remaining need for methods of determining stable operatingconditions for gas fluidized bed polymerization with condensing agents,to facilitate design of the plant and the determination of suitableprocess conditions for suitable or maximum production rates in a givenplant design. Furthermore, because reactor conditions vary with timethere is a need for processes in the production of polyolefins in a gasphase reactor which allow real-time calculation of the ratio of CAs usedin condensed phase cooling.

SUMMARY

This disclosure provides methods for controlling condensed phase coolingin a gas phase reactor used to polymerize olefins. In at least oneembodiment, a method includes introducing one or more polymerizationcatalysts and one or more olefin monomers in a gas phase polymerizationreactor. The method includes introducing a first condensing agent and asecond condensing agent in a ratio of first condensing agent to secondcondensing agent. The ratio of the first condensing agent to the secondcondensing agent is calculated by ascertaining a stick limit for a firstcondensing agent, calculating an equivalence factor relating the firstcondensing agent and a second condensing agent, ascertaining a totalallowable condensing agent, and calculating a first amount of the firstcondensing agent removed and replaced by a second amount of the secondcondensing agent. The method includes calculating the dew point limit ofa gas phase composition including the one or more olefin monomers, thefirst condensing agent, and the second condensing agent, producing acalculated dew point limit; and determining if introducing a mixturecomprising the one or more olefin monomers and the condensing agentcomposition would exceed the calculated dew point limit. The methodincludes withdrawing from the gas phase polymerization reactor a gasphase composition including at least a portion of the first condensingagent and the second condensing agent. The method includes condensing aportion of the gas phase composition yielding a condensed stream. Themethod includes recycling at least a portion of the condensed stream tothe gas phase reactor.

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above recited features of the disclosurecan be understood in detail, a more particular description of thedisclosure, briefly summarized above, may be had by reference toimplementations, some of which are illustrated in the appended drawings.It is to be noted, however, that the appended drawings illustrate onlytypical implementations of this disclosure and are therefore not to beconsidered limiting of scope, for the disclosure may admit to otherequally effective implementations.

FIG. 1 is a schematic diagram of a gas phase polymerization system,according to one embodiment.

FIG. 2 is a diagram of a control system for controlling a gas phasepolymerization process, according to one embodiment.

FIG. 3 is a comparison of gas phase polymerization in dry mode, enhanceddry mode, and condensed mode, according to one embodiment.

FIG. 4 is a plot of equivalence factors as determined by randomlygenerated test conditions, according to one embodiment.

FIG. 5 is a graph of partial pressure of condensing agent versus upperstickiness temperature, according to one embodiment.

FIG. 6 is a graph of mole percentages of condensing agent over time in areactor under conditions where the CA composition is automaticallyadjusted and conditions without automatic adjustment of the CAcomposition, according to one embodiment.

FIG. 7 is a graph of total condensing agent composition versus predictedproduction rate, according to one embodiment.

FIG. 8 is a graph illustrating data generated from commercial processengineering simulation software showing amount of iC5 removed andreplaced by an amount of iC4 versus production rate relative to runninga gas phase polymerization with only iC5, according to one embodiment.

FIG. 9 is a graph illustrating data generated from commercial processengineering simulation software showing amount of iC5 removed andreplaced by an amount of nC4 versus production rate relative to runninga gas phase polymerization with only iC5, according to one embodiment.

FIG. 10 is a graph illustrating production rates for two CA compositionscontaining two CAs, and the production rate of a CA compositioncontaining three CAs, according to one embodiment.

FIG. 11 is a graph illustrating production rates for two different CAcompositions each containing two CAs, and the production rate of a CAcomposition containing three CAs, according to one embodiment.

FIG. 12 is a graph illustrating production rates for two different CAcompositions each containing two CAs, and the production rate of a CAcomposition containing three CAs, according to one embodiment.

FIG. 13 is a graph illustrating production rates for four different CAcompositions each containing two CAs.

FIG. 14 is a graph illustrating production rates versus total mol % ofCAs in the reactor for five different CA compositions each containingtwo CAs, according to one embodiment.

FIG. 15 is a graph illustrating production rates versus total mol % ofCAs in the reactor for eight different CA compositions each containingtwo CAs, according to one embodiment.

FIG. 16 is a graph illustrating the upper stickiness temperature, thelower stickiness temperature, and the stick limit based on partialpressure of iC5 versus sticking temperature, according to one embodiment

FIG. 17 is a graph illustrating production rates versus total allowableCA composition at varying equivalence factors relating iC5 and iC4,according to one embodiment

FIG. 18 is a graph illustrating gas phase composition dew point versustotal allowable CA composition at varying equivalence factors relatingiC5 and iC4, according to one embodiment

FIG. 19 is a graph illustrating the production rates versus totalallowable CA composition comparing the stick limit to the dew pointlimit, according to one embodiment

To facilitate understanding, identical reference numerals have beenused, where possible, to designate identical elements that are common tothe drawings. It is contemplated that elements and features of oneimplementation may be beneficially incorporated in other implementationswithout further recitation.

DETAILED DESCRIPTION

The present disclosure relates to processes for production ofpolyolefins in a gas phase reactor using condensing agent(s) (CAs), andreal-time calculation of the ratio of one type of CA to another CAwithin a CA composition. The use of condensed phase cooling allows forincreased production rates as compared to dry mode cooling because theheat of vaporization of the liquid portion of the recycle streamincreases cooling capacity. The use of more than a single CA may allowfor even greater cooling because individual CAs have different effectson the stickiness temperatures of the polymer being formed within thereactor. In order to avoid reactor shutdown and operation undersuboptimal conditions, a method to adjust the ratio of CAs entering thepolymerization reactor should be accomplished in real-time. It has beendiscovered that the calculation and use of a suitable ratio of CAs mayimprove the polymer production rate. In addition to improving polymerproduction rate, a suitable ratio of CAs may help avoid a concentrationof CA composition that is too high and exceeds the SL. Furthermore, asuitable ratio of CAs may allow for greater temperature variationwithout falling below the DPL. Additionally, the concentration of CAs ina CA composition may be varied to adjust both the SL (based onconcentration of CA composition) and the DPL (based on temperature).Calculation and use of a suitable ratio of CAs may be accomplished inreal-time by ascertaining the SL for a first CA, ascertaining theequivalence of one or more additional CAs and the first CA, determiningthe dew point limit of the gas phase composition, adjusting theequivalence factor or the SL, and calculating a ratio of CAs within a CAcomposition. It has been discovered that contrary to typical practices,improved production can be achieved not by reducing the quantity of CAcomposition within a reactor or by venting the reactor to decreasepressure, but instead by adjusting the concentration of CAs within a CAcomposition.

The methods described may maintain or reduce gas phase composition dewpoint during polyolefin polymerization by adjusting the ratio ofdifferent CAs within a CA composition. Additionally, increased coolingcan be achieved while maintaining or reducing gas phase composition dewpoint by increasing total allowable CA composition at calculated ratiosof CAs within a CA composition. The balance of individual types of CA ina CA composition reduces or eliminates the “stickiness” drawbacks ofexcessive CA composition concentrations. Further, the make-up of the CAcomposition can be changed in real-time as reactor conditions changeaccording to dew point calculations, equivalence factors relating afirst CA and one or more additional CAs, and the stick limit of thefirst CA in order to achieve higher polyolefin production.

Definitions

The term “CA” refers to a condensing agent. “CAs” refers to condensingagents. “CA composition” refers to the total condensing agent in thereactor and encompasses compositions with two or more condensing agents.CAs suitable for use in methods of the present disclosure may includeC3-C6 hydrocarbons or combinations thereof. For example, CAs suitablefor use may include n-butane, isobutane, n-pentane, isopentane,neo-pentane, hexane, isohexane, and other hydrocarbon compounds that aresimilarly non-reactive in the polymerization process. A “binary CAcomposition” is a CA composition that includes two CAs, and a “ternaryCA composition” is a CA composition that includes three CAs.

The terms “iC4” and “isobutane” refer to 2-methylpropane.

The terms “nC4” and “n-butane” refer to normal-butane.

The terms “iC5” and “isopentane” refer to 2-methylbutane.

The terms “nC5” and “n-pentane” refer to normal-pentane.

The terms “neoC5” and “neo-pentane” refer to 2,2-dimethylpropane.

The terms “nC6” and “n-hexane” refer to normal-hexane.

The term “C6 inerts” refers to various hexane isomers that are inert toreaction conditions and may include nC6, 2-methylpentane,3-methylpentane, 2,2-dimethyl butane, 2,3-dimethylbutane, 2-hexene,and/or 3-hexene.

The term “dew point” means the temperature at which condensation of acomponent in the recycle gas or gas phase composition first begins. Thedew point temperature is pressure dependent. As the pressure in thereactor is increased the dew point temperature will increase. Also, thedew point takes into account temperature, pressure and physicalproperties of other gases in gaseous mixtures. At a temperature at orbelow the dew point of a component in the gaseous medium, a component inthe liquid phase may not evaporate or vaporize into the gaseous medium.On the other hand, a liquid phase component may vaporize or evaporate ifthe temperature of the gaseous medium is above the dew point.

“Linear low density polyethylene” (LLDPE) is polyethylene in anoverlapping density range, i.e., 0.890 to 0.930 g/cm³, typically from0.915 to 0.930 g/cm³, that is linear and is substantially free of longchain branching. LLDPE can be produced with conventional Ziegler-Nattacatalysts, vanadium catalysts, or with metallocene catalysts in gasphase reactors and/or in slurry reactors and/or in solution reactors.“Linear” means that the polyethylene is substantially free of long chainbranches, typically referred to as a branching index (g′_(vis)) of 0.97or above, or 0.98 or above. Branching index, g′_(vis), is measured asdescribed below.

As used herein, Mn is number average molecular weight, Mw is weightaverage molecular weight, and Mz is z average molecular weight, wt % isweight percent, and mol % is mole percent. Molecular weight distribution(MWD), also referred to as polydispersity index (PDI), is defined to beMw divided by Mn. Unless otherwise noted, all molecular weights (e.g.,Mw, Mn, Mz) are reported in units of g/mol.

The term “real-time” means data processed and systems adjusted, withoutintentional delay, given the processing limitations of the system andthe time to accurately measure the data.

With reference to a product being produced by a continuous reaction, theexpression “instantaneous” value of a property of the product denotesthe value of the property of the most recently produced quantity of theproduct. The most recently produced quantity typically undergoes mixingwith previously produced quantities of the product before a mixture ofthe recently and previously produced product exits the reactor. Incontrast, with reference to a product being produced by a continuousreaction, “average” (or “bed average”) value (at a time “T”) of aproperty denotes the value of the property of the product that exits thereactor at time T.

The term “polyethylene” denotes a polymer of ethylene and optionally oneor more C3-C18 alpha-olefins, while the term “polyolefin” denotes apolymer of one or more C2-C18 alpha-olefins and optionally one or morecomonomers. An “olefin” is an unsaturated hydrocarbon that contains atleast one carbon-carbon double bond. An alpha-olefin is a hydrocarbonthat contains at least one carbon-carbon double bond at one end of acarbon chain (e.g. 1-butene, vinyl-cyclohexane). For the purposes ofthis disclosure, ethylene shall be considered an α-olefin.

The term “melt index” refers to a measure of the use of flow of the meltof the thermoplastic polymer. Melt index may be measured according toASTM D1238-13 at suitable weight and temperature. Generally, the meltindex of polyolefins is measured at 2.16 kg at 190° C., 5 kg at 190° C.,or 21.6 kg at 190° C.

Polymerization Reactor

The methods described may be used in pilot plant or commercial sizereactors including a variety of designs. For example, the model can beused in commercial-scale reactions, such as gas-phase fluidized-bedpolymerization reactions, that can be monitored and optionally alsocontrolled. Some such reactions can occur in a reactor having thegeometry of the fluidized bed reactor 101 discussed with respect toFIG. 1. In other embodiments, a reactor is monitored and optionally alsocontrolled while operating to perform polymerization using any of avariety of different processes (e.g., slurry or gas phase processes).

Generally, in a fluidized gas bed process used for producing polymers, agaseous stream containing one or more monomers is continuously cycledthrough a fluidized bed in the presence of a catalyst under reactiveconditions. A portion of the gaseous stream is withdrawn from thefluidized bed and recycled back into the reactor as a recycle stream.Simultaneously, polymer product is withdrawn from the reactor and freshmonomer and catalyst are added to replace the polymerized monomer andspent catalyst. (See, for example, U.S. Pat. Nos. 4,543,399; 4,588,790;5,028,670; 5,317,036; 5,352,749; 5,405,922; 5,436,304; 5,453,471;5,462,999; 5,616,661; and 5,668,228; all of which are incorporated byreference.)

FIG. 1 is a schematic diagram of a polymerization system 100 that can bemonitored and controlled in accordance with embodiments described. Thepolymerization system 100 includes a fluidized bed reactor 101. Thefluidized bed reactor 101 has a bottom end 103, a straight section 105,a top expanded section 107, and a distributor plate 109 within thestraight section 105. A fluidized bed 111 of granular polymer (onceformed) and catalyst particles is contained within the straight section105, and may optionally extend slightly into the top expanded section107. The bed is fluidized by the steady flow of a gas stream includingrecycle gas through the distributor plate 109. The gas stream entersfluidized bed reactor through line 113, additional reaction and inertgases (including CAs) may be added in adjustable ratios through line115. Aluminum alkyl (optional) may be added through line 117. The flowrate of the gas stream is regulated to maintain circulation of fluidizedbed 111. In some embodiments, a recycle gas velocity of from about 1ft/sec to about 3 ft/sec, such as from about 2 ft/sec to about 3 ft/sec,or from about 2.4 ft/sec to about 2.8 ft/sec is used to maintain afluidized bed 111 in the reactor 101 while operating the reactor 101 ata total pressure of about 4200 kPa or less, about 700 kPa to about 4200kPa, about 1300 kPa to about 2800 kPa, or about 1700 kPa to about 2500kPa. The mixture of gases in the reactor is a gas phase composition.

The polymerization system 100 has one or more catalyst lines 119 forcontrolling the addition of polymerization catalyst to a reaction zone(not shown) within fluidized bed 111, and generally within straightsection 105. Within the reaction zone, the catalyst particles react withreaction gases including an olefin monomer (e.g., ethylene) andoptionally a comonomer and other reaction gases (e.g., hydrogen) toproduce the granular polymer particles. As new polymer particles areproduced, other polymer particles are continually withdrawn from thefluidized bed 111 through a product discharge line 121 to productrecovery system 123. The fluidized bed 111 may be maintained at aconstant height by withdrawing a portion of the fluidized bed 111 at arate equal to the rate of formation of particulate product. The productmay be removed continuously or nearly continuously via a series ofvalves (not shown) into a fixed volume chamber (not shown), which issimultaneously vented back to the reactor. The fixed volume chamber andventing back to the reactor allows for highly efficient removal of theproduct, while recycling a large portion of the unreacted gases back tothe reactor.

Unreacted olefins and CA composition within the product recovery systemmay be removed via line 125, compressed in compressor 127, and travelvia line 129 to heat exchanger 131 to be cooled before being recycled(e.g., via line 133) to line 113. The particles within product recoverysystem 123 may be degassed (or “purged”) with a flow of inert gas suchas nitrogen through line 135 to remove substantially all of thedissolved hydrocarbon materials. In some instances, the polymer granulesmay be treated with a small stream of humidified nitrogen to deactivatetrace quantities of residual catalyst. The purge gas may be removed vialine 137 to be vented to flare or recycled with further processing.

The polymerization system 100 also has a cooling loop which includes afirst recycle gas line 139, compressor 141, a second recycle gas line143, and cooling system 145 (such as a circulating gas cooler), coupledwith the fluidized bed reactor 101. Cooling system 145 may acceptcooling water via line 147 and expel heated water via line 149. Coolingof the recycle gas is a method used to cool polymerization system 100 toreduce or eliminate issues that may arise from exothermic polyolefinproduction. During operation, the cooled circulating gas from coolingsystem 145 flows via line 113 through inlet 151 into the fluidized bedreactor 101, then propagates upward through fluidized bed 111 and outfrom the fluidized bed reactor 102 via outlet 153.

The top expanded section 107 may also be known as a “velocity reductionzone,” and is designed to reduce the quantities of particle entrainmentin the recycle gas line from the fluidized bed. The diameter of the topexpanded section 107 generally increases with the distance from straightsection 105. The increased diameter causes a reduction in the speed ofthe gas stream, which allows most of the entrained particles to settleback into the fluidized bed 111, thereby minimizing the quantities ofsolid particles that are “carried over” from the fluidized bed 111through the recycle gas line 139. In some instances, a screen (notshown) may be included upstream of the compressor 141 to remove largermaterial.

To maintain a reactor temperature, the temperature of the recycle gasmay be continuously adjusted up or down to accommodate changes in therate of heat generation due to the polymerization. One or moretemperature sensors 155 may be located in the fluidized bed, and usedwith a control system and the cooling loop to control the temperature ofthe fluidized bed 111 near the process set-point. A heated portion ofthe gas phase composition, which carries heat energy from the fluidizedbed reactor 101, is withdrawn from the outlet 153 and is pumped by thecompressor 141 via line 143 to cooling system 145 where the temperatureof the heated reactor gas is reduced and at least a portion of the CAcomposition present is condensed to a liquid. The recycle gas from thecooling system 145, including condensed liquids, flows via line 113 tothe reactor inlet 151 to cool the fluidized bed 111. Temperature sensors(not shown) near the inlet and outlet of the cooling system 145 mayprovide feedback to a control system (not shown) to regulate the amountby which cooling system 145 reduces the temperature of the gas streamentering the fluidized bed reactor 101.

The fluidized bed reactor 101 may also include skin temperature sensors157, mounted in positions along a wall of the straight section 105 ofthe fluidized bed reactor 101 so as to protrude into the bed from thereactor wall by a small amount (e.g., about one eighth to one quarter ofan inch). The skin temperature sensors 157 may be configured andpositioned to sense the temperature of the resin near the wall of thefluidized bed reactor 101 during operation.

The temperature sensors 155 in the fluidized bed 111 can include aresistance temperature sensor positioned and configured to sense bedtemperature during reactor operation at a location within the fluidizedbed reactor 101 away from the reactor wall. The resistance temperaturesensor can be mounted so as to protrude into the bed more deeply thanthe skin temperature sensors 157 (e.g., about 8 to 18 inches away fromthe reactor wall).

Other sensors and other apparatuses may be employed to measure otherreaction parameters during a polymerization reaction. The reactionparameters may include instantaneous and bed-averaged resin productproperties (e.g., melt index and density of the polymer resin productbeing produced by the polymerization system 100 during a polymerizationreaction). Resin product properties may be measured by periodicallysampling the resin when exiting the reactor (e.g., about once per hour),and performing the appropriate tests in a quality control laboratory.

Other measured reaction parameters may include reactor gas composition(e.g., concentrations and partial pressures of reactant gases, CA, andother inert gases, such as nitrogen, inert hydrocarbon, and the like).The gas phase composition within the reactor may be measured by removalof gas from upper portion 107 via line 159 to a gas chromatograph (“GC”)system 161. GC system 161 may also be connected by lines (not shown)other than line 159 to other parts of polymerization system 100, such asrecycle gas line 139, compressor 141, line 143 or any combinationthereof.

The process control variables may be controlled to obtain increasedproductivity for the polymerization system 100 and particular propertiesfor the resin. For example, the parameters used to control gas phasecomposition within the fluidized bed reactor 101 can include theconcentration (partial pressure) and composition of the CA compositionand comonomer, the partial pressure of monomer, the type and propertiesof catalysts, and the temperature of the reaction process. Additionally,a polymerization reaction during a transition from production of acertain grade of polyolefin to a different grade may be controlled bycontrolling process control variables to ensure that the product (e.g.,the granular resin) has properties compliant with an initialspecification set at the start of the transition, the product producedduring the transition ceases to comply with the initial specificationset at a first time, and the product has properties compliant with afinal specification set at the end of the transition. In the methodsdescribed, stickiness of the resin during the reaction may be controlledby a control system adjusting (or regulating) the temperature and/or thecomposition and concentration of the CA composition used in thereaction.

FIG. 2 is a block diagram of a control system 200 that can be used tocontrol the polymerization system 100. The control system 200 may be adistributed control system (DCS), a direct digital controller (DDC), aprogrammable logic controller (PLC), or other suitable systems orcombination of systems. The control system 200 has a processor 201 thatimplements machine readable instructions from a storage system 203.Illustrative processors may include a single core processor, a multiplecore processor, a virtual processor, a virtual processor in a cloudimplementation, an application specific integrated circuit (ASIC), or acombination of these systems. Illustrative storage systems 203 caninclude random access memory (RAM), read only memory (ROM), hard drives,virtual hard drives, RAM drives, cloud storage systems, optical storagesystems, physically encoded instructions (for example, in an ASIC), or acombination of these systems.

Adjustments to control settings may be determined based on the input ofdata from temperature sensors 155 and 157, the GC 161, and lab data 205,among others. After determining new control settings, the control system200 may make in real time, or recommend, adjustments, for example, tothe process cooling systems 207, the CA addition and recycling systems209, flow control systems 211, and termination systems 213, amongothers.

The reactor and associated methods may be an element of a staged reactoremploying two or more reactors in series, where one reactor may produce,for example, a high molecular weight polyolefin and another reactor mayproduce a low molecular weight polyolefin.

The cooled recycle gas may provide for exemplary non-limitingembodiments of cooling of the polymerization system. For example, theability to cool the polymerization system may have a direct correlationwith the heat capacity of the recycle gas, known as “dry mode.” It ispossible to add inert gases to the recycle gas with greater heatcapacity which improves the cooling, but direct correlation with theheat capacity can be maintained to cool the polymerization system in“enhanced dry mode.” Additionally or alternatively, the dry modes can bedeviated from by cooling the recycle gas past its dew point andcondensing a portion of the gas to a liquid. The liquid has greaterability to cool the polymerization system than the gas because of theliquid's heat of vaporization. An example of the difference in coolingcapacity is shown in FIG. 3, comparing cooling in different embodiments.Line 301 represents the dew point of the recycle gas within apolymerization system. Under dry conditions (represented by line 303),the recycle gas provides cooling of the reactor in direct relation tothe temperature to which it is cooled. In enhanced dry mode (representedby line 305), the addition of inert gases to the recycle gas allows forslightly greater reactor cooling based on the temperature to which it iscooled in the cooling system. Lastly, line 307 represents condensedphase cooling, which allows even greater cooling by the addition ofcondensing agents, or inert gases that are condensed past the dew pointand therefore have more ability to cool the reactor because of theirheat of vaporization.

Polyolefin Production

Polyolefin polymerization may be performed by contacting in a reactor(such as the fluidized bed reactor 101 of FIG. 1) an olefin monomer(optionally with a comonomer) with one or more catalysts (supported ornot) in the presence of CA composition and optionally hydrogen. Theindividual flow rates of olefin monomer, optional comonomer, optionalhydrogen, and CA composition (or individual components thereof) may becontrolled to maintain fixed gas composition targets. The concentrationof all gases may be measured with a chromatograph. A solid catalyst, acatalyst slurry, or liquid solution of the catalyst(s) may be injecteddirectly into the reactor using a carrier gas (e.g., purified nitrogen),where the feed rate of catalyst(s) may be adjusted to change or maintainthe catalyst inventory in the reactor.

In some embodiments, the polymerization reaction may be performed at areactor pressure of about 4200 kPa or less, about 700 kPa to about 4200kPa, about 1300 kPa to about 2800 kPa, or about 1700 kPa to about 2500kPa.

Generally, the olefin monomer concentration is controlled and monitoredby the olefin monomer partial pressure. In some embodiments, the olefinpartial pressure may be at about 4200 kPa or less, such as about 500 kPato about 2000 kPa, about 1000 kPa to about 1800 kPa, about 1200 kPa toabout 1700 kPa, or about 1400 kPa to about 1600 kPa.

The comonomer concentration may be controlled and monitored by acomonomer to olefin monomer mole ratio (or alternatively, the flow ratesof comonomer and olefin monomer are held at a fixed ratio). Whenpresent, the comonomer may be at a relative concentration to the olefinmonomer that will achieve the desired weight percent incorporation ofthe comonomer into the finished polyolefin. In some embodiments, thecomonomer may be present with the olefin monomer in a mole ratio in thegas phase of from about 0.0001 to about 50 (comonomer to olefinmonomer), from about 0.0001 to about 5, from about 0.0005 to about 1.0,or from about 0.001 to about 0.5.

The olefin monomer or comonomers, for example, may be a C2-C18alpha-olefin. In some embodiments, the olefin monomer is ethylene, and acomonomer is a C3-C12 alpha olefin. In some embodiments, the olefinmonomer may be ethylene or propylene, and a comonomer may include C4-C10alpha-olefins. For example C2-C18 alpha-olefins that may be utilized asa comonomer in embodiments described may include: ethylene, propylene,1-butene, 1-pentene, 1-hexene, 1-heptene, 1-octene, 4-methylpent-1-ene,1-decene, 1-dodecene, 1-hexadecene, and the like, and a combinationthereof. Additionally, a polyene may be used as a comonomer according tosome embodiments described. For example, polyenes may include:1,3-hexadiene, 1,4-hexadiene, cyclopentadiene, dicyclopentadiene,4-vinylcyclohex-1-ene, methyloctadiene, 1-methyl-1,6-octadiene,7-methyl-1,6-octadiene, 1,5-cyclooctadiene, norbornadiene, ethylidenenorbornene, 5-vinylidene-2-norbornene, 5-vinyl-2-norbornene, and olefinsformed in situ in the polymerization medium. When olefins are formed insitu in the polymerization medium, the formation of polyolefinscontaining long chain branching may occur. Additional examples ofcomonomers may include isoprene, styrene, butadiene, isobutylene,chloroprene, acrylonitrile, and cyclic olefins. Combinations of theforegoing may be utilized in the methods described.

Examples of polymers that can be produced in accordance with the methoddescribed may include the following: homopolymers and copolymers ofC2-C18 alpha olefins; polyvinyl chlorides, ethylene propylene rubbers(EPRs); ethylene-propylene diene rubbers (EPDMs); polyisoprene;polystyrene; polybutadiene; polymers of butadiene copolymerized withstyrene; polymers of butadiene copolymerized with isoprene; polymers ofbutadiene with acrylonitrile; polymers of isobutylene copolymerized withisoprene; ethylene butene rubbers and ethylene butene diene rubbers;polychloroprene; norbornene homopolymers and copolymers with one or moreC2-C18 alpha olefin; and terpolymers of one or more C2-C18 alpha olefinswith a diene. In some embodiments, the polyolefin produced by the methoddescribed may include olefin homopolymers (e.g., homopolymers ofethylene or propylene). In some instances, the polyolefin produced maybe copolymers, terpolymers, and the like of the olefin monomer and thecomonomer.

In some embodiments, the polyolefin produced may be a polyethylene or apolypropylene. Exemplary polyethylenes produced by the methods describedmay be homopolymers of ethylene or copolymers of ethylene (orterpolymers of ethylene) having at least one alpha-olefin (comonomer)where the ethylene content may be at least about 50% by weight of thetotal monomers involved. Exemplary polypropylenes produced by themethods described may be homopolymers of propylene or interpolymers ofpropylene and at least one alpha-olefin (comonomer) where the propylenecontent may be at least about 50% by weight of the total monomersinvolved.

Hydrogen gas is often used in olefin polymerization to control the finalproperties of the polyolefin. For some types of catalyst systems,increasing concentrations (or partial pressures) of hydrogen may alterthe molecular weight or melt index of the polyolefin generated. The meltindex can thus be influenced by the hydrogen concentration. Generally,the amount of hydrogen in the polymerization is expressed as a moleratio relative to the total polymerizable monomer (e.g., relative toethylene or relative to a blend of ethylene and hexene or propylene).The amount of hydrogen used in some polymerization processes is anamount necessary to achieve the desired melt index (or molecular weight)of the final polyolefin resin. In some embodiments, the mole ratio inthe gas phase of hydrogen to total polymerizable monomer (H₂ to monomer)may be about 0.00001 or greater, about 0.0005 or greater, about 0.001 orgreater, about 10 or less, about 5 or less, about 3 or less, or about0.10 or less, where a range may include a combination of a upper moleratio with a lower mole ratio described.

Catalysts

Exemplary catalysts suitable for use in the embodiments described mayinclude: Ziegler Natta catalysts, chromium based catalysts, vanadiumbased catalysts (e.g., vanadium oxychloride and vanadiumacetylacetonate), metallocene catalysts and other single-site orsingle-site-like catalysts, cationic forms of metal halides (e.g.,aluminum trihalides), anionic initiators (e.g., butyl lithiums), cobaltcatalysts and mixtures thereof, nickel catalysts and mixtures thereof,rare earth metal catalysts (i.e., those containing a metal having anatomic number in the Periodic Table of 57 to 103), such as compounds ofcerium, lanthanum, praseodymium, gadolinium and neodymium. A singlecatalyst may be used, or a mixture of catalysts may be employed, ifdesired. The catalyst may be soluble or insoluble, supported orunsupported. Further, the catalyst may be a prepolymer, spray dried withor without a filler, a liquid, or a solution, slurry/suspension, ordispersion.

Metallocenes may include “half sandwich” and “full sandwich” compoundshaving one or more pi-bonded ligands (e.g. cyclopentadienyl and ligandsisolobal to cyclopentadienyl) bound to at least one Group 3 to Group 12metal atom (Including the Lanthanide series and Actinide serieselements), and one or more leaving groups bound to the at least onemetal atom. The metallocene may be supported on a support material, andmay be supported with or without another catalyst component.

The pi-bonded ligands may be one or more rings or ring systems, such ascycloalkadienyl ligands and heterocyclic analogues. The pi-bondedligands are distinct from the leaving groups bound to the catalystcompound in that they are not highly susceptible to substitution orabstraction reactions. If a metallocene catalyst has more than onepi-bonded ligand they may be the same or different, either or both ofwhich may contain heteroatoms and either or both of which may besubstituted by at least one R group. Non-limiting examples ofsubstituent R groups include groups selected from hydrogen radicals,alkyls, alkenyls, alkynyls, cycloalkyls, aryls, acyls, aroyls, alkoxys,aryloxys, alkylthiols, dialkylamines, alkylamidos, alkoxycarbonyls,aryloxycarbonyls, carbomoyls, alkyl- and dialkyl-carbamoyls, acyloxys,acylaminos, aroylaminos, and combinations thereof. In some embodiments,pi-bonded ligands are (independently in the case of multiple) selectedfrom cyclopentadienyl, indenyl, tetrahydroindenyl, fluorenyl, andsubstituted derivatives of each. In relation to hydrocarbonsubstituents, the term “substituted” means that the group following thatterm possesses at least one moiety in place of one or more hydrogens,which moieties are selected from such groups as halogen radicals (e.g.,Cl, F, Br), hydroxyl groups, carbonyl groups, carboxyl groups, aminegroups, phosphine groups, alkoxy groups, phenyl groups, naphthyl groups,C1 to C10 alkyl groups, C2 to C10 alkenyl groups, and combinationsthereof. Examples of substituted alkyls and aryls may include: acylradicals, alkylamino radicals, alkoxy radicals, aryloxy radicals,alkylthio radicals, dialkylamino radicals, alkoxycarbonyl radicals,aryloxycarbonyl radicals, carbomoyl radicals, alkyl- anddialkyl-carbamoyl radicals, acyloxy radicals, acylamino radicals,arylamino radicals, and combinations thereof.

In some embodiments, each leaving group may be independently selectedfrom halogen ions, hydrides, C1-12 alkyls, C2-12 alkenyls, C6-12 aryls,C7-20 alkylaryls, C1-12 alkoxys, C6-16 aryloxys, C7-18 alkylaryloxys,C1-12 fluoroalkyls, C6-12 fluoroaryls, and C1-12 heteroatom-containinghydrocarbons, and substituted derivatives thereof. The phrase “leavinggroup” refers to one or more chemical moieties bound to the metal centerof the catalyst component, which can be abstracted from the catalystcomponent by an activator, thus producing a species active towardsolefin polymerization or oligomerization.

The structure of the metallocene catalyst compound may take on manyforms, such as those disclosed in, for example, U.S. Pat. Nos.5,026,798, 5,703,187, and 5,747,406, including a dimer or oligomericstructure, such as disclosed in, for example, U.S. Pat. Nos. 5,026,798and 6,069,213. Others include those catalysts described in U.S. PatentApplication Publication Nos. US2005/0124487A1, US2005/0164875A1, andUS2005/0148744. In some embodiments, the metallocene may be formed witha hafnium metal atom (e.g., bis(n-propylcyclopentadienyl) hafnium Xn,bis(n-butylcyclopentadienyl) hafnium Xn, orbis(n-pentylcyclopentadienyl) hafnium Xn, where X is one of chloride orfluoride and n is 2), such as is described in U.S. Pat. Nos. 6,242,545and 7,157,531.

In certain embodiments, the metallocene catalysts compounds describedabove may include their structural or optical or enantiomeric isomers(racemic mixture), and, in some embodiments, may be a pure enantiomer.

In some embodiments, the catalyst may be a metallocene catalyst in theabsence of, or essentially free of, scavengers (e.g., triethylaluminum,trimethylaluminum, tri-isobutylaluminum, tri-n-hexylaluminum, diethylaluminum chloride, dibutyl zinc and the like). The term “essentiallyfree” means that the compounds are not deliberately added to the reactoror reactor components, and if present, are present in less than about 1ppm in the reactor.

In some embodiments, the catalysts may be used with cocatalysts andpromoters (e.g., alkylaluminums, alkylaluminum halides, alkylaluminumhydrides, and aluminoxanes).

In some embodiments, the one or more catalysts may be combined with upto about 10 wt % of one or more antistatic agents, such as a metal-fattyacid compound (e.g., an aluminum stearate), based upon the weight of thecatalyst system (or its components). Other metals that may be suitableinclude other Group 2 and Group 5-13 metals. One or more antistaticagents may be added directly to the reactor system as well.

In some embodiments, supported catalyst(s) may be combined withactivators by tumbling and/or other suitable means, optionally with upto about 2.5 wt % (by weight of the catalyst composition) of anantistatic agent. Exemplary antistatic agent may include: an ethoxylatedor methoxylated amine (e.g., KEMAMINE AS-990, available from ICISpecialties) and polysulfone copolymers in the OCTASTAT family ofcompounds, more specifically Octastat 2000, 3000, and 5000 (availablefrom Octel).

In some embodiments, the antistatic agent may be mixed with the catalystand fed into the reactor. In other embodiments, the antistatic agent maybe fed into the reactor separate from the catalyst. One advantage offeeding an anti-static agent o the reactor separate from the catalyst isthat it permits on-line adjustment of the level of the additive. Theantistatic agents may individually be in a solution, slurry, or as asolid (e.g. as a powder) before introduction into the reactor.

In various embodiments, a polymerization reaction according to themethods described may optionally employ other additives, such as inertparticulate particles.

In some embodiments, the polymerization reaction temperature may beabout 30° C. to about 120° C., about 60° C. to about 115° C., about 70°C. to about 110° C., or about 70° C. to about 105° C.

In at least one embodiment, the present disclosure provides a catalystsystem comprising a catalyst compound having a metal atom. The catalystcompound can be a metallocene catalyst compound. The metal can be aGroup 3 through Group 12 metal atom, such as Group 3 through Group 10metal atoms, or lanthanide Group atoms. The catalyst compound having aGroup 3 through Group 12 metal atom can be monodentate or multidentate,such as bidentate, tridentate, or tetradentate, where a heteroatom ofthe catalyst, such as phosphorous, oxygen, nitrogen, or sulfur ischelated to the metal atom of the catalyst. Non-limiting examplesinclude bis(phenolate)s. In at least one embodiment, the Group 3 throughGroup 12 metal atom is selected from Group 5, Group 6, Group 8, or Group10 metal atoms. In at least one embodiment, a Group 3 through Group 10metal atom is selected from Cr, Sc, Ti, Zr, Hf, V, Nb, Ta, Mn, Re, Fe,Ru, Os, Co, Rh, Ir, and Ni. In at least one embodiment, a metal atom isselected from Groups 4, 5, and 6 metal atoms. In at least oneembodiment, a metal atom is a Group 4 metal atom selected from Ti, Zr,or Hf. The oxidation state of the metal atom can range from 0 to +7, forexample +1, +2, +3, +4, or +5, for example +2, +3 or +4.

A catalyst compound of the present disclosure can be a chromium orchromium-based catalyst. Chromium-based catalysts include chromium oxide(CrO₃) and silylchromate catalysts. Chromium catalysts have been thesubject of much development in the area of continuous fluidized-bedgas-phase polymerization for the production of polyethylene polymers.Such catalysts and polymerization processes have been described, forexample, in U.S. Patent Application Publication No. 2011/0010938 andU.S. Pat. Nos. 7,915,357, 8,129,484, 7,202,313, 6,833,417, 6,841,630,6,989,344, 7,504,463, 7,563,851, 8,420,754, and 8,101,691.

Metallocene catalyst compounds as used herein include metallocenescomprising Group 3 to Group 12 metal complexes, for example, Group 4 toGroup 6 metal complexes, for example, Group 4 metal complexes. Themetallocene catalyst compound of catalyst systems of the presentdisclosure may be unbridged metallocene catalyst compounds representedby the formula: Cp^(A)Cp^(B)M′X′_(n), wherein each Cp^(A) and Cp^(B) isindependently selected from cyclopentadienyl ligands and ligandsisolobal to cyclopentadienyl, one or both Cp^(A) and Cp^(B) may containheteroatoms, and one or both Cp^(A) and Cp^(B) may be substituted by oneor more R″ groups. M′ is selected from Groups 3 through 12 atoms andlanthanide Group atoms. X′ is an anionic leaving group. n is 0 or aninteger from 1 to 4. R″ is selected from alkyl, lower alkyl, substitutedalkyl, heteroalkyl, alkenyl, lower alkenyl, substituted alkenyl,heteroalkenyl, alkynyl, lower alkynyl, substituted alkynyl,heteroalkynyl, alkoxy, lower alkoxy, aryloxy, alkylthio, loweralkylthio, arylthio, aryl, substituted aryl, heteroaryl, aralkyl,aralkylene, alkaryl, alkarylene, haloalkyl, haloalkenyl, haloalkynyl,heteroalkyl, heterocycle, heteroaryl, a heteroatom-containing group,hydrocarbyl, lower hydrocarbyl, substituted hydrocarbyl,heterohydrocarbyl, silyl, boryl, phosphino, phosphine, amino, amine,ether, and thioether.

In at least one embodiment, each Cp^(A) and Cp^(B) is independentlyselected from cyclopentadienyl, indenyl, fluorenyl,cyclopentaphenanthreneyl, benzindenyl, fluorenyl, octahydrofluorenyl,cyclooctatetraenyl, cyclopentacyclododecene, phenanthrindenyl,3,4-benzofluorenyl, 9-phenylfluorenyl, 8-H-cyclopent[a]acenaphthylenyl,7-H-dibenzofluorenyl, indeno[1,2-9]anthrene, thiophenoindenyl,thiophenofluorenyl, and hydrogenated versions thereof.

The metallocene catalyst compound may be a bridged metallocene catalystcompound represented by the formula: Cp^(A)(A)Cp^(B)M′X′_(n), whereineach Cp^(A) and Cp^(B) is independently selected from cyclopentadienylligands and ligands isolobal to cyclopentadienyl. One or both Cp^(A) andCp^(B) may contain heteroatoms, and one or both Cp^(A) and Cp^(B) may besubstituted by one or more R″ groups. M′ is selected from Groups 3through 12 atoms and lanthanide Group atoms. X′ is an anionic leavinggroup. n is 0 or an integer from 1 to 4. (A) is selected from divalentalkyl, divalent lower alkyl, divalent substituted alkyl, divalentheteroalkyl, divalent alkenyl, divalent lower alkenyl, divalentsubstituted alkenyl, divalent heteroalkenyl, divalent alkynyl, divalentlower alkynyl, divalent substituted alkynyl, divalent heteroalkynyl,divalent alkoxy, divalent lower alkoxy, divalent aryloxy, divalentalkylthio, divalent lower alkylthio, divalent arylthio, divalent aryl,divalent substituted aryl, divalent heteroaryl, divalent aralkyl,divalent aralkylene, divalent alkaryl, divalent alkarylene, divalenthaloalkyl, divalent haloalkenyl, divalent haloalkynyl, divalentheteroalkyl, divalent heterocycle, divalent heteroaryl, a divalentheteroatom-containing group, divalent hydrocarbyl, divalent lowerhydrocarbyl, divalent substituted hydrocarbyl, divalentheterohydrocarbyl, divalent silyl, divalent boryl, divalent phosphino,divalent phosphine, divalent amino, divalent amine, divalent ether,divalent thioether. R″ is selected from alkyl, lower alkyl, substitutedalkyl, heteroalkyl, alkenyl, lower alkenyl, substituted alkenyl,heteroalkenyl, alkynyl, lower alkynyl, substituted alkynyl,heteroalkynyl, alkoxy, lower alkoxy, aryloxy, alkylthio, loweralkylthio, arylthio, aryl, substituted aryl, heteroaryl, aralkyl,aralkylene, alkaryl, alkarylene, haloalkyl, haloalkenyl, haloalkynyl,heteroalkyl, heterocycle, heteroaryl, a heteroatom-containing group,hydrocarbyl, lower hydrocarbyl, substituted hydrocarbyl,heterohydrocarbyl, silyl, boryl, phosphino, phosphine, amino, amine,germanium, ether, and thioether.

In at least one embodiment, each of Cp^(A) and Cp^(B) is independentlyselected from cyclopentadienyl, n-propylcyclopentadienyl, indenyl,pentamethylcyclopentadienyl, tetramethylcyclopentadienyl, andn-butylcyclopentadienyl. (A) may be 0, S, NR′, or SiR′₂, where each R′is independently hydrogen or C₁-C₂₀ hydrocarbyl.

In another embodiment, the metallocene catalyst compound is representedby the formula:

T_(y)Cp_(m)MG_(n)X_(q)

where Cp is independently a substituted or unsubstitutedcyclopentadienyl ligand or substituted or unsubstituted ligand isolobalto cyclopentadienyl such as indenyl, fluorenyl and indacenyl. M is aGroup 4 transition metal. G is a heteroatom group represented by theformula JR*_(Z) where J is N, P, O or S, and R* is a linear, branched,or cyclic C₁-C₂₀ hydrocarbyl. z is 1 or 2. T is a bridging group. y is 0or 1. X is a leaving group. m=1, n=1, 2 or 3, q=0, 1, 2 or 3, and thesum of m+n+q is equal to the oxidation state of the transition metal.

In at least one embodiment, J is N, and R* is methyl, ethyl, propyl,butyl, pentyl, hexyl, heptyl, octyl, nonyl, cyclooctyl, cyclododecyl,decyl, undecyl, dodecyl, adamantyl or an isomer thereof.

The metallocene catalyst compound may be selected from:

-   bis(1-methyl, 3-n-butyl cyclopentadienyl) zirconium dichloride;-   dimethylsilyl bis(tetrahydroindenyl) zirconium dichloride;-   bis(n-propylcyclopentadienyl) hafnium dimethyl;-   dimethylsilyl    (tetramethylcyclopentadienyl)(cyclododecylamido)titanium dimethyl;-   dimethylsilyl    (tetramethylcyclopentadienyl)(cyclododecylamido)titanium dichloride;-   dimethylsilyl (tetramethylcyclopentadienyl)(t-butylamido)titanium    dimethyl;-   dimethylsilyl (tetramethylcyclopentadienyl)(t-butylamido)titanium    dichloride;-   μ-(CH₃)₂Si(cyclopentadienyl)(1-adamantylamido)M(R)₂;-   μ-(CH₃)₂Si(3-tertbutylcyclopentadienyl)(1-adamantylamido)M(R)₂;-   μ-(CH₃)₂(tetramethylcyclopentadienyl)(1-adamantylamido)M(R)₂;-   μ-(CH₃)₂Si(tetramethylcyclopentadienyl)(1-adamantylamido)M(R)₂;-   μ-(CH₃)₂C(tetramethylcyclopentadienyl)(1-adamantylamido)M(R)₂;-   μ-(CH₃)₂Si(tetramethylcyclopentadienyl)(1-tertbutylamido)M(R)₂;-   μ-(CH₃)₂Si(fluorenyl)(1-tertbutylamido)M(R)₂;-   μ-(CH₃)₂Si(tetramethylcyclopentadienyl)(1-cyclododecylamido)M(R)₂;-   μ-(C₆H₅)₂C(tetramethylcyclopentadienyl)(1-cyclododecylamido)M(R)₂;-   μ-(CH₃)₂Si(η⁵-2,6,6-trimethyl-1,5,6,7-tetrahydro-s-indacen-1-yl)(tertbutylamido)M(R)₂;    where M is selected from Ti, Zr, and Hf; and R is selected from    halogen or C₁ to C₅ alkyl.

In at least one embodiment, the catalyst compound is a bis(phenolate)catalyst compound represented by Formula (I):

M is a Group 4 metal. X¹ and X² are independently a univalent C₁-C₂₀hydrocarbyl, C₁-C₂₀ substituted hydrocarbyl, a heteroatom or aheteroatom-containing group, or X¹ and X² join together to form a C₄-C₆₂cyclic or polycyclic ring structure. R¹, R², R³, R⁴, R⁵, R⁶, R⁷, R⁸, R⁹,and R¹⁰ is independently hydrogen, C₁-C₄₀ hydrocarbyl, C₁-C₄₀substituted hydrocarbyl, a heteroatom or a heteroatom-containing group,or two or more of R¹, R², R³, R⁴, R⁵, R⁶, R⁷, R⁸, R⁹, or R¹⁰ are joinedtogether to form a C₄-C₆₂ cyclic or polycyclic ring structure, or acombination thereof. Q is a neutral donor group. J is heterocycle, asubstituted or unsubstituted C₇-C₆₀ fused polycyclic group, where atleast one ring is aromatic and where at least one ring, which may or maynot be aromatic, has at least five ring atoms. G is as defined for J ormay be hydrogen, C₂-C₆₀ hydrocarbyl, C₁-C₆₀ substituted hydrocarbyl, ormay independently form a C₄-C₆₀ cyclic or polycyclic ring structure withR⁶, R⁷, or R⁸ or a combination thereof. Y is divalent C₁-C₂₀ hydrocarbylor divalent C₁-C₂₀ substituted hydrocarbyl or (-Q*-Y—) together form aheterocycle. Heterocycle may be aromatic and/or may have multiple fusedrings.

In at least one embodiment, the catalyst compound represented by Formula(I) is:

where M is Hf, Zr, or Ti. X¹, X², R¹, R², R³, R⁴, R⁵, R⁶, R⁷, R⁸, R⁹,R¹⁰, and Y are as defined for Formula (I). R¹¹, R¹², R¹³, R¹⁴, R¹⁵, R¹⁶,R¹⁷, R¹⁸, R¹⁹, R²⁰, R²¹, R²², R²³, R²⁴, R²⁵, R²⁶, R²⁷, and R²⁸ isindependently a hydrogen, C₁-C₄₀ hydrocarbyl, C₁-C₄₀ substitutedhydrocarbyl, a functional group comprising elements from Groups 13 to17, or two or more of R¹, R², R³, R⁴, R⁵, R⁶, R⁷, R⁸, R⁹, R¹⁰, R¹¹, R¹²,R¹³, R¹⁴, R¹⁵, R¹⁶, R¹⁷, R¹⁸, R¹⁹, R²⁰, R²¹, R²², R²³, R²⁴, R²⁵, R²⁶,R²⁷, and R²⁸ may independently join together to form a C₄-C₆₂ cyclic orpolycyclic ring structure, or a combination thereof. R¹¹ and R¹² mayjoin together to form a five- to eight-membered heterocycle. Q* is agroup 15 or 16 atom. z is 0 or 1. J* is CR″ or N, and G* is CR″ or N,where R″ is C₁-C₂₀ hydrocarbyl or carbonyl-containing C₁-C₂₀hydrocarbyl. z=0 if Q* is a group 16 atom, and z=1 if Q* is a group 15atom.

In at least one embodiment the catalyst is an iron complex representedby formula (IV):

wherein:A is chlorine, bromine, iodine, —CF₃ or —OR′,each of R¹ and R² is independently hydrogen, C₁-C₂₂-alkyl,C₂-C₂₂-alkenyl, C₆-C₂₂-aryl, arylalkyl where alkyl has from 1 to 10carbon atoms and aryl has from 6 to 20 carbon atoms, or five-, six- orseven-membered heterocyclyl comprising at least one atom selected fromthe group consisting of N, P, O and S;wherein each of R¹ and R² is optionally substituted by halogen, —NR¹¹ ₂,—OR¹¹ or —SiR¹² ₃;wherein R¹ optionally bonds with R³, and R² optionally bonds with R⁵, ineach case to independently form a five-, six- or seven-membered ring;R⁷ is a C₁-C₂₀ alkyl;each of R³, R⁴, R⁵, R⁸, R⁹, R¹⁰, R¹⁵, R¹⁶, and R¹⁷ is independentlyhydrogen, C₁-C₂₂-alkyl, C₂-C₂₂-alkenyl, C₆-C₂₂-aryl, arylalkyl wherealkyl has from 1 to 10 carbon atoms and aryl has from 6 to 20 carbonatoms, —NR¹¹ ₂, —OR¹¹, halogen, —SiR¹² ₃ or five-, six- orseven-membered heterocyclyl comprising at least one atom selected fromthe group consisting of N, P, O and S;wherein R³, R⁴, R⁵, R⁷, R⁸, R⁹, R¹⁰, R¹⁵, R¹⁶, and R¹⁷ are optionallysubstituted by halogen, —NR¹¹ ₂, —OR¹¹ or —SiR¹² ₃;wherein R³ optionally bonds with R⁴, R⁴ optionally bonds with R⁵, R⁷optionally bonds with R¹⁰, R¹⁰ optionally bonds with R⁹, R⁹ optionallybonds with R⁸, R¹⁷ optionally bonds with R¹⁶, and R¹⁶ optionally bondswith R¹⁵, in each case to independently form a five-, six- orseven-membered carbocyclic or heterocyclic ring, the heterocyclic ringcomprising at least one atom from the group consisting of N, P, O and S;R¹³ is C₁-C₂₀-alkyl bonded with the aryl ring via a primary or secondarycarbon atom,R¹⁴ is chlorine, bromine, iodine, —CF₃ or —OR″, or C₁-C_(m)-alkyl bondedwith the aryl ring; each R¹¹ is independently hydrogen, C₁-C₂₂-alkyl,C₂-C₂₂-alkenyl, C₆-C₂₂-aryl, arylalkyl where alkyl has from 1 to 10carbon atoms and aryl has from 6 to 20 carbon atoms, or —SiR¹² ₃,wherein R¹¹ is optionally substituted by halogen, or two R¹¹ radicalsoptionally bond to form a five- or six-membered ring;each R¹² is independently hydrogen, C₁-C₂₂-alkyl, C₂-C₂₂-alkenyl,C₆-C₂₂-aryl, arylalkyl where alkyl has from 1 to 10 carbon atoms andaryl has from 6 to 20 carbon atoms, or two R¹² radicals optionally bondto form a five- or six-membered ring,each of E¹, E², and E³ is independently carbon, nitrogen or phosphorus;each u is independently 0 if E¹, E², and E³ is nitrogen or phosphorusand is 1 if E¹, E², and E³ is carbon,each X is independently fluorine, chlorine, bromine, iodine, hydrogen,C₁-C₂₀-alkyl, C₂-C₁₀-alkenyl, C₆-C₂₀-aryl, arylalkyl where alkyl hasfrom 1 to 10 carbon atoms and aryl has from 6 to 20 carbon atoms, —NR¹⁸₂, OR¹⁸, SR¹⁸, —SO₃R¹⁸, —OC(O)R¹⁸, —CN, —SCN, β-diketonate, —CO, —BF₄ ⁻,—PF₆ ⁻ or bulky non-coordinating anions, and the radicals X can bebonded with one another;each R¹⁸ is independently hydrogen, C₁-C_(m)-alkyl, C₂-C₂₀-alkenyl,C₆-C₂₀-aryl, arylalkyl where alkyl has from 1 to 10 carbon atoms andaryl has from 6 to 20 carbon atoms, or —SiR¹⁹ ₃, wherein R¹⁸ can besubstituted by halogen or nitrogen- or oxygen-containing groups and twoR¹⁸ radicals optionally bond to form a five- or six-membered ring;each R¹⁹ is independently hydrogen, C₁-C₂₀-alkyl, C₂-C₂₀-alkenyl,C₆-C₂₀-aryl or arylalkyl where alkyl has from 1 to 10 carbon atoms andaryl has from 6 to 20 carbon atoms, wherein R¹⁹ can be substituted byhalogen or nitrogen- or oxygen-containing groups or two R¹⁹ radicalsoptionally bond to form a five- or six-membered ring;s is 1, 2, or 3,D is a neutral donor, andt is 0 to 2.

In at least one embodiment, the catalyst is a quinolinyldiamidotransition metal complex represented by formulas (V) and (VI):

wherein:M is a Group 3-12 metal;J is a three-atom-length bridge between the quinoline and the amidonitrogen;E is selected from carbon, silicon, or germanium;X is an anionic leaving group;L is a neutral Lewis base;R¹ and R¹³ are independently selected from the group consisting ofhydrocarbyls, substituted hydrocarbyls, and silyl groups;R² through R¹² are independently selected from the group consisting ofhydrogen, hydrocarbyls, alkoxy, silyl, amino, aryloxy, substitutedhydrocarbyls, halogen, and phosphino;n is 1 or 2;m is 0, 1, or 2n+m is not greater than 4; andany two adjacent R groups (e.g. R¹ & R², R² & R³, etc.) may be joined toform a substituted or unsubstituted hydrocarbyl or heterocyclic ring,where the ring has 5, 6, 7, or 8 ring atoms and where substitutions onthe ring can join to form additional rings;any two X groups may be joined together to form a dianionic group;any two L groups may be joined together to form a bidentate Lewis base;an X group may be joined to an L group to form a monoanionic bidentategroup.In at least one embodiment M is a Group 4 metal, zirconium or hafnium;In at least one embodiment J is an arylmethyl, dihydro-1H-indenyl, ortetrahydronaphthalenyl group;In at least one embodiment E is carbon;In at least one embodiment X is alkyl, aryl, hydride, alkylsilane,fluoride, chloride, bromide, iodide, triflate, carboxylate, oralkylsulfonate;In at least one embodiment L is an ether, amine or thioether;In at least one embodiment, R⁷ and R⁸ are joined to form a six memberedaromatic ring with the joined R⁷R⁸ group being —CH═CHCH═CH—;In at least one embodiment R¹⁰ and R¹¹ are joined to form a fivemembered ring with the joined R¹⁰ and R¹¹ groups being —CH₂CH₂—; In atleast one embodiment, R¹⁰ and R¹¹ are joined to form a six membered ringwith the joined R¹⁰ and R¹¹ groups being —CH₂CH₂CH₂—.In at least one embodiment, R¹ and R¹³ may be independently selectedfrom phenyl groups that are variously substituted with between zero tofive substituents that include F, Cl, Br, I, CF₃, NO₂, alkoxy,dialkylamino, aryl, and alkyl groups having 1 to 10 carbons, such asmethyl, ethyl, propyl, butyl, pentyl, hexyl, heptyl, octyl, nonyl,decyl, and isomers thereof.

In some embodiments, the catalyst is a phenoxyimine compound representedby the formula (VII):

wherein M represents a transition metal atom selected from the groups 3to 11 metals in the periodic table; k is an integer of 1 to 6; m is aninteger of 1 to 6; R^(a) to R^(f) may be the same or different from oneanother and each represent a hydrogen atom, a halogen atom, ahydrocarbon group, a heterocyclic compound residue, an oxygen-containinggroup, a nitrogen-containing group, a boron-containing group, asulfur-containing group, a phosphorus-containing group, asilicon-containing group, a germanium-containing group or atin-containing group, among which 2 or more groups may be bound to eachother to form a ring; when k is 2 or more, R^(a) groups, R^(b) groups,R^(c) groups, R^(d) groups, R^(e) groups, or R^(f) groups may be thesame or different from one another, one group of R^(a) to R^(f)contained in one ligand and one group of R^(a) to R^(f) contained inanother ligand may form a linking group or a single bond, and aheteroatom contained in R^(a) to R^(f) may coordinate with or bind to M;m is a number satisfying the valence of M; Q represents a hydrogen atom,a halogen atom, an oxygen atom, a hydrocarbon group, anoxygen-containing group, a sulfur-containing group, anitrogen-containing group, a boron-containing group, analuminum-containing group, a phosphorus-containing group, ahalogen-containing group, a heterocyclic compound residue, asilicon-containing group, a germanium-containing group or atin-containing group; when m is 2 or more, a plurality of groupsrepresented by Q may be the same or different from one another, and aplurality of groups represented by Q may be mutually bound to form aring.

In another embodiment, the catalyst is a bis(imino)pyridyl of theformula (VIII):

wherein:M is Co or Fe; each X is an anion; n is 1, 2 or 3, so that the totalnumber of negative charges on said anion or anions is equal to theoxidation state of a Fe or Co atom present in (VIII);R¹, R² and R³ are each independently hydrogen, hydrocarbyl, substitutedhydrocarbyl, or an inert functional group;R⁴ and R⁵ are each independently hydrogen, hydrocarbyl, an inertfunctional group or substituted hydrocarbyl;R⁶ is formula (IX):

and R⁷ is formula (X):

R⁸ and R¹³ are each independently hydrocarbyl, substituted hydrocarbylor an inert functional group;R⁹, R¹⁰, R¹¹, R¹⁴, R¹⁵ and R¹⁶ are each independently hydrogen,hydrocarbyl, substituted hydrocarbyl or an inert functional group;R¹² and R¹⁷ are each independently hydrogen, hydrocarbyl, substitutedhydrocarbyl or an inert functional group;and provided that any two of R⁸, R⁹, R¹⁰, R¹¹, R¹², R¹³, R¹⁴, R¹⁵, R¹⁶and R¹⁷ that are adjacent to one another, together may form a ring.

In at least one embodiment, the catalyst compound is represented by theformula (XI):

M¹ is selected from the group consisting of titanium, zirconium,hafnium, vanadium, niobium, tantalum, chromium, molybdenum and tungsten.In at least one embodiment, M¹ is zirconium. Each of Q¹, Q², Q³, and Q⁴is independently oxygen or sulfur. In at least one embodiment, at leastone of Q¹, Q², Q³, and Q⁴ is oxygen, alternately all of Q¹, Q², Q³, andQ⁴ are oxygen.R¹ and R² are independently hydrogen, halogen, hydroxyl, hydrocarbyl, orsubstituted hydrocarbyl (such as C₁-C₁₀ alkyl, C₁-C₁₀ alkoxy, C₆-C₂₀aryl, C₆-C₁₀ aryloxy, C₂-C₁₀ alkenyl, C₂-C₄₀ alkenyl, C₇-C₄₀ arylalkyl,C₇-C₄₀ alkylaryl, C₈-C₄₀ arylalkenyl, or conjugated diene which isoptionally substituted with one or more hydrocarbyl, tri(hydrocarbyl)silyl or tri(hydrocarbyl) silylhydrocarbyl, the diene having up to 30atoms other than hydrogen). R¹ and R² can be a halogen selected fromfluorine, chlorine, bromine, or iodine. In at least one embodiment, R¹and R² are chlorine.

Alternatively, R¹ and R² may also be joined together to form analkanediyl group or a conjugated C₄-C₄₀ diene ligand which iscoordinated to M¹. R¹ and R² may also be identical or differentconjugated dienes, optionally substituted with one or more hydrocarbyl,tri(hydrocarbyl) silyl or tri(hydrocarbyl) silylhydrocarbyl, the dieneshaving up to 30 atoms not counting hydrogen and/or forming a π-complexwith M′.

Exemplary groups suitable for R¹ and or R² can include 1,4-diphenyl,1,3-butadiene, 1,3-pentadiene, 2-methyl 1,3-pentadiene, 2,4-hexadiene,1-phenyl, 1,3-pentadiene, 1,4-dibenzyl, 1,3-butadiene,1,4-ditolyl-1,3-butadiene, 1,4-bis(trimethylsilyl)-1,3-butadiene, and1,4-dinaphthyl-1,3-butadiene. R¹ and R² can be identical and are C₁-C₃alkyl or alkoxy, C₆-C₁₀ aryl or aryloxy, C₂-C₄ alkenyl, C₇-C₁₀arylalkyl, C₇-C₁₂ alkylaryl, or halogen.

Each of R⁴, R⁵, R⁶, R⁷, R⁸, R⁹, R¹⁰, R¹¹, R¹², R¹³, R¹⁴, R¹⁵, R¹⁶, R¹⁷,R¹⁸, and R¹⁹ is independently hydrogen, halogen, C₁-C₄₀ hydrocarbyl orC₁-C₄₀ substituted hydrocarbyl (such as C₁-C₁₀ alkyl, C₁-C₁₀ alkoxy,C₆-C₂₀ aryl, C₆-C₁₀ aryloxy, C₂-C₁₀ alkenyl, C₂-C₄₀ alkenyl, C₇-C₄₀arylalkyl, C₇-C₄₀ alkylaryl, C₅-C₄₀ arylalkenyl, or conjugated dienewhich is optionally substituted with one or more hydrocarbyl,tri(hydrocarbyl) silyl or tri(hydrocarbyl) silylhydrocarbyl, the dienehaving up to 30 atoms other than hydrogen), —NR′₂, —SR, —OR, —OSiR′₃,—PR′₂, where each R is hydrogen, halogen, C₁-C₁₀ alkyl, or C₆-C₁₀ aryl,or one or more of R⁴ and R⁵, R⁵ and R⁶, R⁶ and R⁷, R⁸ and R⁹, R⁹ andR¹⁰, R¹⁰ and R¹¹, R¹² and R¹³, R¹³ and R¹⁴, R¹⁴ and R¹⁵, R¹⁶ and R¹⁷,R¹⁷ and R¹⁸, and R¹⁸ and R¹⁹ are joined to form a saturated ring,unsaturated ring, substituted saturated ring, or substituted unsaturatedring. In at least one embodiment, C₁-C₄₀ hydrocarbyl is selected frommethyl, ethyl, propyl, n-propyl, isopropyl, n-butyl, isobutyl,sec-butyl, n-pentyl, isopentyl, sec-pentyl, n-hexyl, isohexyl,sec-hexyl, n-heptyl, isoheptyl, sec-heptyl, n-octyl, isooctyl,sec-octyl, n-nonyl, isononyl, sec-nonyl, n-decyl, isodecyl, andsec-decyl.

In at least one embodiment, R¹¹ and R¹² are C₆-C₁₀ aryl such as phenylor naphthyl optionally substituted with C₁-C₄₀ hydrocarbyl, such asC₁-C₁₀ hydrocarbyl. In at least one embodiment, R⁶ and R¹⁷ are C₁₋₄₀alkyl, such as C₁-C₁₀ alkyl.

In at least one embodiment, each of R⁴, R⁵, R⁶, R⁷, R⁸, R⁹, R¹⁰, R¹³,R¹⁴, R¹⁵, R¹⁶, R¹⁷, R¹⁸, and R¹⁹ is independently hydrogen or C₁-C₄₀hydrocarbyl. In at least one embodiment, C₁-C₄₀ hydrocarbyl is selectedfrom methyl, ethyl, propyl, n-propyl, isopropyl, n-butyl, isobutyl,sec-butyl, n-pentyl, isopentyl, sec-pentyl, n-hexyl, isohexyl,sec-hexyl, n-heptyl, isoheptyl, sec-heptyl, n-octyl, isooctyl,sec-octyl, n-nonyl, isononyl, sec-nonyl, n-decyl, isodecyl, andsec-decyl. In at least one embodiment, each of R⁶ and R¹⁷ is C₁-C₄₀hydrocarbyl and R⁴, R⁵, R⁷, R⁸, R⁹, R¹⁰, R¹³, R¹⁴, R¹⁵, R¹⁶, R¹⁸, andR¹⁹ is hydrogen. In at least one embodiment, C₁-C₄₀ hydrocarbyl isselected from methyl, ethyl, propyl, n-propyl, isopropyl, n-butyl,isobutyl, sec-butyl, n-pentyl, isopentyl, sec-pentyl, n-hexyl, isohexyl,sec-hexyl, n-heptyl, isoheptyl, sec-heptyl, n-octyl, isooctyl,sec-octyl, n-nonyl, isononyl, sec-nonyl, n-decyl, isodecyl, andsec-decyl.

R³ is a C₁-C₄₀ unsaturated alkyl or substituted C₁-C₄₀ unsaturated alkyl(such as C₁-C₁₀ alkyl, C₁-C₁₀ alkoxy, C₆-C₂₀ aryl, C₆-C₁₀ aryloxy,C₂-C₁₀ alkenyl, C₂-C₄₀ alkenyl, C₇-C₄₀ arylalkyl, C₇-C₄₀ alkylaryl,C₈-C₄₀ arylalkenyl, or conjugated diene which is optionally substitutedwith one or more hydrocarbyl, tri(hydrocarbyl) silyl or tri(hydrocarbyl)silylhydrocarbyl, the diene having up to 30 atoms other than hydrogen).

In at least one embodiment, R³ is a hydrocarbyl comprising a vinylmoiety. As used herein,

“vinyl” and “vinyl moiety” are used interchangeably and include aterminal alkene, e.g. represented by the structure

Hydrocarbyl of R³ may be further substituted (such as C₁-C₁₀ alkyl,C₁-C₁₀ alkoxy, C₆-Cao aryl, C₆-C₁₀ aryloxy, C₂-C₁₀ alkenyl, C₂-C₄₀alkenyl, C₇-C₄₀ arylalkyl, C₇-C₄₀ alkylaryl, C₈-C₄₀ arylalkenyl, orconjugated diene which is optionally substituted with one or morehydrocarbyl, tri(hydrocarbyl) silyl or tri(hydrocarbyl)silylhydrocarbyl, the diene having up to 30 atoms other than hydrogen).In at least one embodiment, R³ is C₁-C₄₀ unsaturated alkyl that is vinylor substituted C₁-C₄₀ unsaturated alkyl that is vinyl. R³ can berepresented by the structure —R′CH═CH₂ where R′ is C₁-C₄₀ hydrocarbyl orC₁-C₄₀ substituted hydrocarbyl (such as C₁-C₁₀ alkyl, C₁-C₁₀ alkoxy,C₆-C₂₀ aryl, C₆-C₁₀ aryloxy, C₂-C₁₀ alkenyl, C₂-C₄₀ alkenyl, C₇-C₄₀arylalkyl, C₇-C₄₀ alkylaryl, C₈-C₄₀ arylalkenyl, or conjugated dienewhich is optionally substituted with one or more hydrocarbyl,tri(hydrocarbyl) silyl or tri(hydrocarbyl) silylhydrocarbyl, the dienehaving up to 30 atoms other than hydrogen). In at least one embodiment,C₁-C₄₀ hydrocarbyl is selected from methyl, ethyl, propyl, n-propyl,isopropyl, n-butyl, isobutyl, sec-butyl, n-pentyl, isopentyl,sec-pentyl, n-hexyl, isohexyl, sec-hexyl, n-heptyl, isoheptyl,sec-heptyl, n-octyl, isooctyl, sec-octyl, n-nonyl, isononyl, sec-nonyl,n-decyl, isodecyl, and sec-decyl.

In at least one embodiment, R³ is 1-propenyl, 1-butenyl, 1-pentenyl,1-hexenyl, 1-heptenyl, 1-octenyl, 1-nonenyl, or 1-decenyl.

In at least one embodiment, the catalyst is a Group 15-containing metalcompound represented by Formulas (XII) or (XIII):

wherein M is a Group 3 to 12 transition metal or a Group 13 or 14 maingroup metal, a Group 4, 5, or 6 metal. In some embodiments, M is a Group4 metal, such as zirconium, titanium, or hafnium. Each X isindependently a leaving group, such as an anionic leaving group. Theleaving group may include a hydrogen, a hydrocarbyl group, a heteroatom,a halogen, or an alkyl; y is 0 or 1 (when y is 0 group L′ is absent).The term ‘n’ is the oxidation state of M. In various embodiments, n is+3, +4, or +5. In some embodiments, n is +4. The term ‘m’ represents theformal charge of the YZL or the YZL′ ligand, and is 0, −1, −2 or −3 invarious embodiments. In some embodiments, m is −2. L is a Group 15 or 16element, such as nitrogen or oxygen; L′ is a Group 15 or 16 element orGroup 14 containing group, such as carbon, silicon or germanium. Y is aGroup 15 element, such as nitrogen or phosphorus. In some embodiments, Yis nitrogen. Z is a Group 15 element, such as nitrogen or phosphorus. Insome embodiments, Z is nitrogen. R¹ and R² are, independently, a C₁ toC₂₀ hydrocarbon group, a heteroatom containing group having up to twentycarbon atoms, silicon, germanium, tin, lead, or phosphorus. In someembodiments, R¹ and R² are a C₂ to C₂₀ alkyl, aryl or aralkyl group,such as a C₂ to C₂₀ linear, branched or cyclic alkyl group, or a C₂ toC₂₀ hydrocarbon group. R¹ and R² may also be interconnected to eachother. R³ may be absent or may be a hydrocarbon group, a hydrogen, ahalogen, a heteroatom containing group. In some embodiments, R³ isabsent, for example, if L is an oxygen, or a hydrogen, or a linear,cyclic, or branched alkyl group having 1 to 20 carbon atoms. R⁴ and R⁵are independently an alkyl group, an aryl group, substituted aryl group,a cyclic alkyl group, a substituted cyclic alkyl group, a cyclic aralkylgroup, a substituted cyclic aralkyl group, or multiple ring system,often having up to 20 carbon atoms. In some embodiments, R⁴ and R⁵ havebetween 3 and 10 carbon atoms, or are a C₁ to C₂₀ hydrocarbon group, aC₁ to C₂₀ aryl group or a C₁ to C₂₀ aralkyl group, or a heteroatomcontaining group. R⁴ and R⁵ may be interconnected to each other. R⁶ andR⁷ are independently absent, hydrogen, an alkyl group, halogen,heteroatom, or a hydrocarbyl group, such as a linear, cyclic or branchedalkyl group having 1 to 20 carbon atoms. In some embodiments, R⁶ and R⁷are absent. R* may be absent, or may be a hydrogen, a Group 14 atomcontaining group, a halogen, or a heteroatom containing group.

By “formal charge of the YZL or YZL′ ligand,” it is meant the charge ofthe entire ligand absent the metal and the leaving groups X. By “R¹ andR² may also be interconnected” it is meant that R¹ and R² may bedirectly bound to each other or may be bound to each other through othergroups. By “R⁴ and R⁵ may also be interconnected” it is meant that R⁴and R⁵ may be directly bound to each other or may be bound to each otherthrough other groups. An alkyl group may be linear, branched alkylradicals, alkenyl radicals, alkynyl radicals, cycloalkyl radicals, arylradicals, acyl radicals, aroyl radicals, alkoxy radicals, aryloxyradicals, alkylthio radicals, dialkylamino radicals, alkoxycarbonylradicals, aryloxycarbonyl radicals, carbomoyl radicals, alkyl- ordialkyl-carbamoyl radicals, acyloxy radicals, acylamino radicals,aroylamino radicals, straight, branched or cyclic, alkylene radicals, orcombination thereof. An aralkyl group is defined to be a substitutedaryl group.

In one or more embodiments, R4 and R5 are independently a grouprepresented by the following structure (XIV):

wherein R⁸ to R¹² are each independently hydrogen, a C₁ to C₄₀ alkylgroup, a halide, a heteroatom, a heteroatom containing group containingup to 40 carbon atoms. In some embodiments, R⁸ to R¹² are a C₁ to C₂₀linear or branched alkyl group, such as a methyl, ethyl, propyl, orbutyl group. Any two of the R groups may form a cyclic group and/or aheterocyclic group. The cyclic groups may be aromatic. In one embodimentR⁹, R¹⁰ and R¹² are independently a methyl, ethyl, propyl, or butylgroup (including all isomers). In another embodiment, R⁹, R¹⁰ and R¹²are methyl groups, and R⁸ and R¹¹ are hydrogen.

In one or more embodiments, R⁴ and R⁵ are both a group represented bythe following structure (XV):

wherein M is a Group 4 metal, such as zirconium, titanium, or hafnium.In some embodiments, M is zirconium. Each of L, Y, and Z may be anitrogen. Each of R¹ and R² may be —CH₂—CH₂—. R³ may be hydrogen, and R⁶and R⁷ may be absent.

In some embodiments, the maximum amount of alumoxane is up to a5000-fold molar excess Al/M over the catalyst compound (per metalcatalytic site). The minimum alumoxane-to-catalyst-compound is a 1:1molar ratio. Alternate ranges include from 1:1 to 500:1, alternatelyfrom 1:1 to 200:1, alternately from 1:1 to 100:1, or alternately from1:1 to 50:1.

Other catalysts for use in processes of the present disclosure include“non-metallocene complexes” that are defined to be transition metalcomplexes that do not feature a cyclopentadienyl anion or substitutedcyclopentadienyl anion donors (e.g., cyclopentadienyl, fluorenyl,indenyl, methylcyclopentadienyl). Examples of families ofnon-metallocene complexes that may be suitable can include latetransition metal pyridylbisimines (e.g., U.S. Pat. No. 7,087,686), group4 pyridyldiamidos (e.g., U.S. Pat. No. 7,973,116), quinolinyldiamidos(e.g., U.S. Pub. No. 2018/0002352 A1), pyridylamidos (e.g., U.S. Pat.No. 7,087,690), phenoxyimines (e.g., Accounts of Chemical Research 2009,42, 1532-1544), and bridged bi-aromatic complexes (e.g., U.S. Pat. No.7,091,292), the disclosures of which are incorporated herein byreference.

CA Composition

Methods of the present disclosure allow reactor production rates to beincreased as compared to addition of CAs or CA compositions usedpreviously (e.g., by changing the CAs in the CA composition), whileavoiding the conditions in the reactor that may lead to excessivestickiness or the condensation of liquids in the reactor. These methodsuse available processes and may be implemented at plant sites eitheron-line, in process control systems, or off-line (e.g., usingspreadsheets, databases, or application specific programs).

Increasing productivity of the polymerization process may be achieved bycontrolling the relative concentrations of two or more CAs in thereactor (i.e., a mole percent of a CA relative to total reactor gas,which may be derived from the partial pressure of each relative to thetotal pressure in the reactor). The concentrations of the two or moreCAs may be altered according to a relationship of the total allowable CAcomposition, the SL of a first condensing agent (in a gas compositionhaving a single CA) (SL_(CA1)), the equivalence factor relating thefirst CA and additional CA(s), and the dew point limit of the gas phasecomposition.

Dew Point and Dew Point Limit

The dew point is dependent on the concentrations of the various gaseouscomponents in the gas phase composition, and reactor pressure. Becausethe concentrations of gases within the reactor and the reactor pressuremay change as the reaction proceeds, changes in the dew point arecalculated and monitored. The addition of a CA composition to the gasstream entering the reactor affects the dew point of the gas phasecomposition within the reactor.

The estimation of the dew point may include ascertaining theconcentration of various gases within the gas phase composition, whichmay be determined by gas chromatography in real-time. Furthermore, theestimation of dew point may include ascertaining the pressure within thereactor, which may be defined as the pressure of the reactor justupstream of the distributor plate (e.g. 109 in FIG. 1). The pressureupstream of the distributor plate may include (i) the reactor pressureat the top of the reactor, (ii) the pressure head from the bed ofpolymer inside the reactor, and (iii) the pressure drop across thedistributor plate. Defining the reactor pressure in this manner allowsfor a conservative estimate for the dew point because the combination ofpressures yields a higher pressure result than if the pressure weremeasured at another location in the reactor. Alternatively, otherpressure measuring locations may be used, for example, the pressure ofthe gas leaving the top of the reactor. If the pressure is measured atother locations, the dew point limit may be shifted further from theestimated dew point to account for pressure differences across thereactor.

The dew point of a gas phase composition can be estimated using athermodynamic equation of state, such as the Soave/Redlich/Kwong (SRK)equation or the Benedict/Webb/Rubin (BWR) equation. For hydrocarbonmixtures at the temperatures and pressures within a gas phase reactor,the SRK equation may be used to estimate the dew point. Estimating thedew point for the multicomponent mixture may be accomplished by settingthe fugacity of each of the components in the vapor phase equal to itsfugacity in the liquid phase. For each phase the fugacity is definedwith the help of the thermodynamic equation of state used to estimatethe activity coefficients of each component in the liquid phase and alsothe fugacity coefficient in the gas phase.

Because there are several components in the gas phase composition, thereare also several simultaneous equations. The equations may be simplifiedbecause the concentrations of gases within the gas phase composition andthe pressure are measured, and the remaining unknown is the dew pointtemperature. The equations may be solved for dew point temperature by aniterative method, where an arbitrary temperature is used to find themole fractions of the predicted liquid phase. The temperature is altereduntil the sum of the liquid mole fractions is equal to 1. If the sum ofthe liquid mole fractions is not equal to 1, then the calculation isrepeated with a different temperature. This calculation may occur in aniterative manner on a control system (e.g. control system 200, from FIG.2). The dew point may be estimated as soon as results are obtained fromthe on-line GC, or at specified time periods, such as every 5 minutes,10 minutes, 15 minutes, or greater.

Reaching the dew point in a gas phase reactor may result in reactorshutdown. In order to have safe and continuous reactor operation a dewpoint limit is set at a temperature higher than the estimated dew pointof the gas phase composition. For example, the dew point limit may befrom about 0.5° C. higher to about 20° C. higher, from about 1° C.higher to about 15° C. higher, from about 5° C. higher to about 10° C.higher, or from about 1° C. higher to about 5° C. higher than the dewpoint of the gas phase composition. The automation of reactor conditionsincluding adjusting the CA composition may allow for a dew point limitthat is nearer the calculated dew point of the gas phase composition,for example, the dew point limit may be from about 0.5° C. higher toabout 10° C. higher, from about 1° C. higher to about 8° C. higher, orfrom about 4° C. or higher to about 8° C. higher than the calculated dewpoint of the gas phase composition. The dew point limit may be a fixedtemperature from the calculate dew point of the gas phase composition,for example, 15° C. higher, 14° C. higher, 13° C. higher, 12° C. higher,11° C. higher, 10° C. higher, 9° C. higher, 8° C. higher, 7° C. higher,6° C. higher, 5° C. higher, 4° C. higher, 3° C. higher, 2° C. higher, 1°C. higher, or 0.5° C. higher than the calculated dew point of the gasphase composition. Alternatively, the limit may vary in correlation to aspecific reactor condition, for example, the dew point limit mayincrease in difference from the calculated dew point of the gas phasecomposition with increasing reactor pressure.

If pressure is constant, the dew point limit may be represented as aline in a graph comparing temperature and concentration of a first CA.The dew point may be similarly represented as a line at a lowertemperature, e.g. 10° C. lower than the dew point limit.

Total Allowable Condensing Agent Composition

A fluidized bed process is performed where the velocity of the gaseousrecycle stream is sufficient to maintain the reaction zone in afluidized state. In a fluidized bed polymerization process, the amountof fluid circulated to remove the heat of polymerization may be greaterthan the amount of fluid needed for support of the fluidized bed and foradequate mixing of the solids in the fluidized bed. The excess velocityprovides additional gas flow to (and through) the fluid bed foradditional cooling capacity and more intensive mixing of the reactorbed. However, to prevent excessive entrainment of solids in a gaseousstream withdrawn from the fluidized bed, the velocity of the gaseousstream may be regulated.

A fluidized bed within a gas phase reactor may include reactivecomponents, other reagents (anti-slip, anti-static), and inertcomponents including inert gas and CAs. The combination of all thesecomponents can make up 100% of the flow (e.g., of volume or massbalance) of gas in and through a gas phase reactor. The total allowableCA composition (Z) is the amount of the combination of CAs that issubject to the concentration of other components in the fluidized bed.

Therefore, in order to increase Z, a portion of another component of thegas stream may be decreased. An increase in Z may allow for greatercooling of the reactor and therefore increased production rates, but islimited by reactor volume and venting. Substantially all (e.g. 100%) ofthe components entering the reactor leave the reactor either in theproduct stream or the recycle stream. Z is increased by decreasinganother component. For example, an increase in Z may be accomplished bylower quantities of other inert compounds including nitrogen.Alternatively, Z may be increased by using monomer and comonomer feedswith fewer inert impurities, a higher purity feed may allow forincreased addition of CA composition.

The ratio of inert components can be varied, but may be limited byreactor venting. In order to maintain the mass balance for a given inertgas concentration, the inert gas flow into the reactor must equal theinert gas vented from the reactor. Reducing the concentration of inertgas in the reactor may result in more total vent flow. An increased ventflow may result in greater material loss and may also be limited byreactor design. For a given reactor producing a particular grade ofpolyolefin, the minimum inert gas can be ascertained based on a costanalysis balancing the reactor design including limits on vent flow andraw material loss associated with increased production rates related toimproved cooling from a greater quantity of CA composition.

Because the reactive components and other components that aid in productformation may be specific to one embodiment of a desired product, theymay be kept constant. Alternatively, Z may be increased by lowering theconcentration of monomers or comonomers. Without being limited bytheory, reduction of pressures of monomer and comonomer may decrease thecatalyst activity, but it is possible that the cost associated with adecrease in catalyst activity is overcome by the improved productionrates that accompany increased cooling from additional Z.

Furthermore, Z may be increased by increasing the overall reactorpressure. For example, if the individual components are at a specificpartial pressure increasing the total pressure in the reactor wouldtherefore increase pressure available to a CA composition. An increasein pressure of the reactor may be limited by reactor design, feedstockpressures and compression costs, changes in the solubility andstickiness of the products and reactants.

Therefore, the total allowable CA composition may be a cost benefitanalysis of individual options for increasing Z including, but notlimited to removal of portions of other components or reactorpressurization. The cost analysis may take into account many factorsincluding the catalyst activity, feedstock purity and availability,reactor design (in pressure, volume, and venting), product grades, andflow rates sufficient to fluidize the bed. The cost of any of thesefactors may be balanced by increased production rate resulting fromimproved cooling due to additional volume (or pressure) allotted to CAcomposition.

If reactor conditions near the dew point limit of the gas phasecomposition, typically the response is to lower the total allowable CAcomposition or decrease the reactor pressure through venting. Loweringthe total allowable CA composition will decrease the dew point of thegas phase composition by allowing fewer of the less volatile gaseswithin the reactor. Similarly, venting the reactor lowers the partialpressures of the CAs, and also the total pressure within the reactor.Reactor venting is a rapid method that may be used to avoid the dewpoint limit. While both lowering the total allowable CA composition anddecreasing reactor pressure have a deleterious effect on the productionrate, either may be used to avoid reactor shutdown, and subsequent timespent cleaning and restarting. Therefore it may be less expensive tolower total allowable CA composition or vent the reactor than to reachthe dew point limit and cause condensation and resin stickiness.

Stick Limit

There may be limits to the concentrations of condensable gases, whetherCAs, comonomers or combinations thereof, that can be tolerated in thereaction system. Above certain limiting concentrations, the condensablegases can cause a sudden loss of fluidization in the reactor not due tocondensation near the dew point. The loss of fluidization not due tocondensation near the dew point is indicative of the stick limit (SL).The SL is the limit of CA in a CA composition having a single CA, in agas phase reactor under certain conditions. The SL for a specific CA maybe ascertained by a laboratory method or through computational methods.

A suitable laboratory method for determining SL is described in U.S.Pat. No. 10,029,226, incorporated by reference. The method estimates SLby measuring stirrer rotations per minute in an autoclave as thetemperature is increased. As the mixture becomes overly sticky thestirrer stops at a certain temperature. The test can be performed atvarying levels of the condensing agent and the stickiness temperaturecorrelated to the SL as a linear function. The stick limit of aparticular grade of polyolefin is therefore calculated as a linearfunction of multiple laboratory tests determining stickinesstemperature.

Another suitable laboratory method for determining stickiness and SL isdescribed in U.S. Pat. No. 8,273,834, incorporated by reference. Themethod describes the use of melting point depression to determinestickiness, using differential scanning calorimetry and a prediction ofreaction mixture solubility in polyethylene. The SL can be calculated bydetermining the difference between the reaction temperature and the meltinitiation temperature of the polyolefin reaction mixture, also known asthe change in melt initiation temperature (AMIT). The AMIT is anindication of how far the reaction temperature is into a DSC melt curveat reactor conditions.

A suitable computational method is based on modeling phase behavior inpolymer mixtures. Modeling phase behavior in polymer mixtures maypresent a number of complexities. The complexities in modeling phasebehavior may derive from distributions in molecular weight andcomposition of industrially produced polymers, the tendency for some ofthe polymer chains to crystallize in a high density state (while othersremain amorphous) at low temperatures, and the inaccessibility ofcrystalline domains in absorbing solutes. Equilibrium thermodynamicmodels calculate solubility in the amorphous phase, as they are based onequilibrium between species in solution with the polymer (e.g. withinthe amorphous, and not the crystalline phase, as stated above) and thosesame species in a coexisting phase. Therefore, a clear distinctionbetween total (x_(wi) ^(T)) and amorphous (x_(wi) ^(A)) solubility, andperhaps a statement of the crystallinity (C) itself, is involved in thecomparison of experimental and theoretical values. These are related byequation (E-1):

$\begin{matrix}{x_{wi}^{T} = \frac{x_{wi}^{A}}{1 + \frac{{Cx}_{wa}^{A}}{\left( {1 - C} \right)}}} & \left( {E\text{-}1} \right)\end{matrix}$

where x_(wi) is the mass fraction of species i; the ratio of the mass ofspecies i absorbed to the sum of the mass of species i and the mass ofpolymer. Superscript A represents the case where only the amorphous massof the polymer is considered, while the superscript T represents thecase where the total mass of the polymer is considered. x_(wa) ^(A) isthe mass fraction of the polymer on an amorphous basis, and C is thecrystallinity as a mass fraction; the ratio of the mass of crystallinepolymer to the total mass of the polymer.

Simply accounting for such a basis of solubility is not sufficient, asthe presence of crystalline polymers (or more specifically the tiechains connecting them) may affect the quantity of solute that canabsorb within the amorphous phase of the polymer. One method to accountfor this is to apply an activity coefficient accounting for the effectsof such tie chains as in equation (E-2):

y _(i){circumflex over (φ)}_(i) ^(V) =x _(i) ^(A)γ_(i) ^(A){circumflexover (φ)}_(i) ^(Ref)  (E-2)

where ‘V’ represents vapor and ‘A’ represents the mixture of amorphouspolymer and the absorbed species, y_(i) and x_(i) are the mole fractioncompositions of these respective phases. {circumflex over (φ)}_(i) ^(V)is the fugacity coefficient of species i in the vapor phase, while{circumflex over (φ)}_(i) ^(Ref) is the fugacity coefficient of aspecies in an amorphous phase free from elastic constraints. γ_(i) ^(A)accounts for the effects of the elastic constraints on the fugacitycoefficient of a species in an amorphous phase, and hence thesolubility.

The Sako-Wu-Prausnitz Equation Of State (SWP-EOS) may be used as it is asimple cubic EOS applicable to both small (volatile) molecules andpolymers as shown in equation (E-3):

$\begin{matrix}{P = {\frac{{RT}\left( {v + {b\left\{ {c - 1} \right\}}} \right)}{v\left( {v - b} \right)} - \frac{a}{v\left( {v + b} \right)}}} & \left( {E\text{-}3} \right)\end{matrix}$

where P is the pressure, T is the absolute temperature, v is the molarvolume, R is the universal gas constant, and a, b, and c are theattractive, repulsive and degree-of-freedom parameters of the mixtureunder consideration

The expression for the SWP-EOS fugacity coefficients is calculated as inequation (E-4):

$\begin{matrix}{{\ln\left\lbrack {\hat{\varphi}}_{i} \right\rbrack} = {{{- c_{i}}{\ln\left\lbrack \frac{Z - B}{Z} \right\rbrack}} + {c\frac{B_{i}}{\left( {Z - B} \right)}} - {\frac{A}{B}\left\{ {\frac{2{\sum\limits_{m}^{Comps}{A_{im}x_{m}}}}{A} - \frac{B_{i}}{B}} \right\}{\ln\left\lbrack \frac{Z + B}{Z} \right\rbrack}} - {\frac{A}{B}\frac{B_{i}}{\left( {Z + B} \right)}} - {\ln\lbrack Z\rbrack}}} & \left( {E\text{-}4} \right)\end{matrix}$

where the symbol ‘x’ in equation (E-4) represents mole fraction.

For a more accurate determination of solubility there is an elasticcorrection where the activity coefficient is as discussed by Serna etal. J. Appl. Polym. Sci. 2008, 107, 138 and Banaszak et al.Macromolecules 2004, 37, 9139 and is represented by equation (E-5):

$\begin{matrix}{{\ln\left\lbrack \gamma_{i}^{el} \right\rbrack} = \frac{{\frac{\Delta\; h_{poly}^{fus}{\overset{\_}{v}}_{i}}{R{\overset{\_}{v}}_{{poly}\;}}\left( {\frac{1}{T} - \frac{1}{T_{m}}} \right)} - \left( {\phi_{i} - {\chi_{i}\phi_{i}^{2}}} \right)}{\frac{3}{2f\;\phi_{poly}} - 1}} & \left( {E\text{-}5} \right)\end{matrix}$

where:

Δh_(poly) ^(fus)=enthalpy of fusion of the polymer

v _(k)=partial molar volume of species k in the amorphous phase

k=either ‘i’ or ‘poly’

T=absolute temperature

T_(m)=absolute normal melting point of polymer

ϕ_(k)=volume fraction of species k in the amorphous phase

χ_(k)=Flory interaction parameter of species k in the amorphous phase,given by equation (E-6):

$\begin{matrix}{\chi_{i} = {0.34 + {v_{i}^{L}\frac{\left( {\delta_{i} - \delta_{poly}} \right)^{2}}{RT}}}} & \left( {E\text{-}6} \right)\end{matrix}$

where δ_(k)=solubility parameter, given for volatile species by equation(E-7),

$\begin{matrix}{\delta_{k} = \sqrt{\frac{{\Delta\; h_{k}^{vap}} - {RT}}{v_{k}^{L}}}} & \left( {E\text{-}7} \right)\end{matrix}$

while for polyethylene, δ_(poly) was approximated as 16.7 MPa{circumflexover ( )}0.5, and f=fraction of elastically affected chains.

Given a vapor phase of fixed temperature, pressure and composition (y),the solubility can be determined by calculating the composition of theamorphous phase (x). The set of equations to be solved can consist ofthe statements of equilibrium and material balance. These arerepresented by equation (E-8) and equation (E-9):

E _(i)=ln[y _(i)]+ln[{circumflex over (φ)}^(V) _(i)]−ln[n_(i)]−ln[{circumflex over (φ)}^(A) _(i)]−ln[γ^(el) _(i)]=0,i≠poly  (E-8)

MB=Σ _(s=1) ^(Comps) n _(s)−1=0  (E-9)

As indicated, the unknowns in the model are the moles of substancedissolved in the polymer phase. The unknowns are to be considered ‘molenumbers’, which produce corresponding ‘mole fractions’. The materialbalance equation, requiring unit sum of the dissolved mole numbers,reconciles these. The problem can be stated as an unconstrainedoptimization as in equation (E-10):

$\begin{matrix}{{F\lbrack n\rbrack} = {\begin{bmatrix}E \\{MB}\end{bmatrix} = \begin{bmatrix}0 \\0\end{bmatrix}}} & \left( {E\text{-}10} \right)\end{matrix}$

Initial estimates can be generated by setting n_(poly)˜0.05, andn_(j)˜(1−n_(poly))y_(j≠poly), which can subsequently be refined byNewton iteration; equations (E-11) and (E-12):

$\begin{matrix}{{{\Delta\; n_{j}} = {{- H_{ij}^{- 1}}F_{i}}}{{with}\text{:}}} & \left( {E\text{-}11} \right) \\{H_{ij} = \left( \frac{\partial F_{i}}{\partial n_{j}} \right)_{T,P}} & \left( {E\text{-}12} \right)\end{matrix}$

Mole fractions can be converted to mass fractions by using the numberaverage molecular weight (Mn) of the polymer.

While the given model contains a large number of parameters, themajority can be estimated from literature or characterization data.Furthermore, accurate solubility predictions may be made after fittingtwo of the model parameters (f and T_(m)) to experimental data. Ourmethod for parameterization is:

I. For a given polymer, a low and high temperature (typically 50° C. and85° C., respectively) measured isopentane solubility isotherm are usedto fit f and T_(m) simultaneously.II. Low pressure isopentane solubility isotherms are simulated for eachof these polymers at pressures from about 0.01 bar to about 0.8 bar, andat temperatures from about 50° C. to about 90° C.III. For each of these polymers, isopentane Henry constants were derivedat the above temperatures according to equation (E-13):

Fy _(i) P=w _(i) H _(i)  (E-13)

The derived Henry constants allow for a determination of the slope ofln(H) vs. 1/T for each of these polymers.IV. Using the median and standard deviation of the Henry constant slopesidentified using the procedures of roman numerals I through III abovefor a range of polyethylenes, the following objective function wasminimized with respect to f and T_(m) for each polymer.

In other words, a method described identifies a target value of theisopentane Henry constant slope, and then adjusts f and T_(m) tosimultaneously match this target and one isopentane isotherm (85° C. orthe highest value available) for that particular polymer. Instead ofusing two isotherms for each polymer, the target value of the Henryconstant slope can be applied to polymers of a given type (e.g. C4 andC6 linear low density polyethylenes, (LLDPEs) produced in GPPEreactors), and only a single isotherm (unique to each polymer) isinvolved.

CA Equivalence Factor

The term “equivalence factor” refers to a mole to mole relationship of afirst CA to a second CA where one mole of the first CA may be replacedwith a moles of the second CA. To compare two CAs, the second CA is morevolatile than the first CA. For example, in some embodiments, isopentane(less volatile than n-butane) and n-butane may have a CA equivalencefactor of about 1.8 to about 2.5, which means that during polyolefinproduction, 1 mole of isopentane can be replaced with about 1.8 moles toabout 2.5 moles of n-butane while maintaining the same stickinesstemperature. Replacing a portion of isopentane with an equivalent amountof n-butane may increase cooling capacity without causing stickiness andtherefore allow for increased production rate.

It may be possible to use simulations of the process at various reactorconditions to arrive at a ratio of CAs that will allow for highproduction rates. For example, suitable process simulations may beaccomplished using commercial modelling software, such as PRO/IIproduced by SimSci™ or Aspen Plus produced by Aspentech. Each individualset of conditions takes time to prepare and model in a simulation.Therefore, using simulations to determine the ratio of CAs is not onlycostly and labor intensive, but could not be accomplished withoutsubstantial programming efforts in real-time as the reactor is running.

In some instances, the equivalence factor may be related to thesolubility of a first CA in a polyolefin compared to the solubility of asecond CA in the same polyolefin. Without being limited by theory, thestickiness of a polyolefin mixing with a CA composition within a gasphase reactor may be related to the solubility of the CA composition inthe polyolefin. The solubility of a single CA in a polymer is not onlyaffected by many reaction conditions (e.g. pressure, temperature,product density), but also affected by the presence of other CAs,additives, and reaction components. Because the stickiness of thepolyolefin may limit production rate (because of the relationshipbetween production and temperature), the CA composition is a balance ofthe ability to cool the reaction mixture and the solubility of the CAcomposition in the produced polyolefin.

The equivalence factor is calculated from individual solubilities of CAsin the polyolefin under reactor conditions. Because reactor conditionsdiffer for different polyolefins and for different grades of a singlepolyolefin, and because reactor conditions vary with time, thesolubilities and therefore the equivalence factor of two CAs will alsovary. The variance in equivalence factors means that there would need tobe either multitudinous lab experiments and/or computational studiesperformed in order to determine the equivalence factors related toreasonable reactor conditions for each polymer.

The equivalence factor of a first CA and a second CA at specific reactorconditions may be calculated by performing linear regression of thepartial pressure versus the stickiness temperature of each individual CAand dividing the slopes of the lines. The calculation may be repeatedfor various reactor conditions including variance in temperature,pressure, reactant concentration and ratio of included comonomer. Oncesufficient data is collected (either empirically or computationally),the various equivalence factors may be fit to a line to provide anequation that can be used to rapidly calculate the equivalence factorrelating two condensing agents for a given polyolefin under a set ofreactor conditions. The linear regression allows for the equivalencefactor to be calculated in real time as reactor conditions change duringthe polymerization process being performed.

The linear regression of the equivalence factors may provide an equationrelating reactor conditions and composition of the recycle gas to allowfor calculation of equivalence factors as reactor conditions and gascomposition changes. Also before changes are made in the gas compositionsuch a linear regression allows for calculation of the changes inequivalence factors related to the changes in the gas composition, butat current reactor conditions. The linear regression of equivalencefactors may include reactor conditions such as reactor temperature,reactor pressure, resin melt index, and resin density. The linearregression may also include factors related to the gas composition orrecycle gas composition including mole fractions of the olefin monomer,comonomers, inert gases, and CAs or CA compositions.

FIG. 4 is a graph illustrating computation of equivalence factors ofvarious C6-hydrocarbons in relation to iC5. The thermodynamicapproximation of solubility used to calculate stickiness may be used todetermine an equivalence factor for a random set of conditions.

Table 1 provides exemplary, non-limiting equivalence factors for variousCA components.

TABLE 1 CA Equivalence Factor Relative to Isopentane n-butane about 1.8to about 2.5 isobutane about 2.6 to about 3.8 neo-pentane about 1.5 toabout 2 n-pentane about 0.7 to about 1 n-hexane about 0.2 to about 0.5

The concentration of the CA in the reactor (i.e., the mole percent of CAin the reactor or the sum of mole percent of each of the CA componentsas a function of total reactor gas) may change as the CA compositionchanges. For example, using a CA equivalence factor of 2 forn-butane:isopentane, the partial pressure of the CA in the reactor mayincrease as isopentane is replaced with n-butane to achieve a greaterdew point approach temperature and higher polyolefin production rate.Using the same CA equivalence factor, in some instances, the reactor mayhave a maximum polyolefin production rate, which, if exceeded, may bereduced by replacing n-butane with isopentane, which would decrease thepartial pressure of CA in the reactor. Alternatively, the concentrationof CA in the reactor may not change as the CA composition changes.

In some embodiments, the partial pressure of CA in the reactor may be upto about 1400 kPa, such as about 30 kPa to about 1000 kPa, or about 100kPa to about 700 kPa.

In some embodiments, the mole percent of an individual CA componentrelative to total reactor gas may be up to about 50 mol %, such as about1 mol % to about 40 mol %, about 5 mol % to about 30 mol %, or about 10mol % to about 20 mol %.

Calculating CA Composition

Once each of the factors related to the calculation of the ratio ofcondensing agents has been ascertained, then the SL of a first CA(SL_(CA1)) is subtracted from the total allowable CA (Z) and the resultis divided by the equivalence factor relating a second CA to the firstCA (αCA2) less one. According to equation (E-14):

$\begin{matrix}{X = \frac{Z - {SL}_{{CA}\; 1}}{{\alpha\;{CA}\; 2} - 1}} & \left( {E\text{-}14} \right)\end{matrix}$

where X is a first amount of the first condensing agent removed andreplaced by a second amount of the second condensing agent, where thesecond amount is X multiplied by αCA2, Z is the total allowablecondensing agent, SL_(CA1) is the stick limit for the first condensingagent, and αCA2 is the equivalence factor relating the first condensingagent and the second condensing agent. For example, if the totalallowable CA composition was 25 mol %, stick limit of the firstcondensing agent is 17 mol %, the equivalence factor relating the secondcondensing agent and the first condensing agents was 3, then X (thefirst amount of the first condensing agent removed) would be 4 mol % andthe second amount would be 12 mol %.

Because X represents the amount of CA1 that may be removed, X may not beless than zero or greater than SL_(CA1). Because X is constrained insuch a manner, if SL_(CA1) is greater than the total allowable CAcomposition, no change in the CA composition occurs, and X is zero.Furthermore, the constraints on X mean that the equivalence factor maynot be less than one, because X would be negative, and therefore thefirst CA must be less volatile than the second CA.

The linear regression of equivalence factors for a given combination ofCAs allows for calculating in real time the CA composition that wouldallow for improved polymer production. The equations may be programmedinto a control system that allows for adjustments of the reactionconditions as the information from the reactor is processed.

Without being limited by theory, the combination of two CAs in a binaryCA composition may provide greater polymer production than thecombination of more than two CAs. It may be beneficial to polymerproduction rates to reduce or eliminate inert gases not part of thebinary CA composition. Also, the CAs within a binary CA composition thatprovides improved production may vary with reactor conditions andspecifically with total allowable CA composition. When total allowableCA composition is lower, it may favor a CA composition with lessvolatile CAs, and as the total allowable CA composition increases, thebinary CA composition that provides improved production may be acombination of more volatile CAs.

Avoiding Dew Point Limit

Typically, past procedures have included continually increasing the CAcomposition content without using a method to target a specific ratio ofCAs within the CA composition. Eventually, the upper stickinesstemperature (or an artificial upper limit) or the dew point limit isreached and then either the total allowable CA composition would bedecreased or the reactor pressure would be decreased, either one causinga decrease in production rates. Furthermore, a rapid adjustment toeither the total allowable CA composition or reactor pressure may causepolymer produced during the change to not have the desired properties.The same scenario may take place repeatedly but at different ratios ofCAs within a CA composition, but without targeting a ratio of CAs thescenario is unlikely to lead to improved production rates relative toother methods of reducing the dew point.

Furthermore, the calculation of equivalence factor does not take intoaccount the dew point of the gas phase composition, and therefore, theresult of a calculation of CA composition could suggest a CA compositionthat causes reactor temperature to fall below the dew point limit.Falling below the DPL may not be a change in reactor temperature, but anincrease in the DPL temperature. However, it has been discovered thatadjusting the concentration of CAs in a CA composition may be used toavoid stickiness regimes including those below the dew point limit whilealso maintaining improved production rates relative to other methods ofreducing the dew point. Because on-line calculations of reactorconditions may be nearly continuous, adjustments may be made to the CAcomposition while monitoring the dew point to remain in a non-stickingregime (a safe production zone).

It has been discovered that lowering the equivalence factor or the SL ofthe first CA (SL_(CA1)) may bring the reaction conditions into anon-sticking regime within the dew point limit. This can be accomplishedby (i) calculating an equivalence factor and SL_(CA1) for certainreactor conditions, (ii) calculating the concentration of CAs within theCA composition, (iii) calculating the dew point limit for the gas phasecomposition created by that CA composition, and (iv) determining if thereactor temperature is below the dew point limit. If the temperature isnot below the dew point limit, then proceeding with the CA compositionas calculated. If the temperature falls below the dew point limit, then(v) incrementally lowering the equivalence factor or SL_(CA1) from thatdetermined in (i), (vi) recalculating the CA composition, and (iv)recalculating the dew point limit of the gas phase composition createdby the recalculated CA composition from (vi), and (vii) determining ifthe reactor temperature is below the dew point limit. If the reactortemperature falls below the dew point limit, the process of steps (v)through (vii) is repeated until the equivalence factor or SL_(CA1) islow enough that the new dew point limit is lower than the reactortemperature.

Because these calculations may be performed on a computer processor, theincremental reduction of the original calculated equivalence factor orSL_(CA1) may be performed in small increments, such as increments of0.1, 0.05, 0.01, 0.005, or 0.0001 or less. The reduction of equivalencefactor or SL_(CA1) may also decrease the production rate. Therefore,smaller incremental reductions of equivalence factor and SL_(CA1) mayprovide improved production rates because, for a particular binary CAcomposition, a higher equivalence factor or a higher SL_(CA1) improvesproduction rates. Alternatively, to save calculation time, thecalculations relative to dew point and equivalence factor or SL_(CA1)could be repeated in decreasing increments both reducing and increasingthe equivalence factor or SL_(CA1). For example, the initial incrementalreductions could be large, followed by smaller increases until passingthe dew point limit, and then followed by smaller incremental decreasesuntil back in a non-sticking regime, and so on, until the calculationshave narrowed to a pre-specified number of decimal places of theequivalence factor or SL_(CA1) within a non-sticking regime.

It has been discovered that, reducing the equivalence factor or SL_(CA1)in the manner described yields greater polyolefin production rates thandecreasing the total allowable CA composition (Z) or reducing reactorpressure through venting. Typically, as reactor conditions near the dewpoint for a particular gas phase composition, the practice is to reducethe total allowable CA composition or vent the reactor to reducepressure until the reactor conditions are within the dew point limit.This is effective, but causes a greater decrease in production thanadjusting the amounts of individual CAs within a CA composition. A smalldecrease in the calculated equivalence factor or SL_(CA1) may cause aslight drop in cooling ability and therefore a slight decrease inproduction rate, whereas decreasing the total allowable CA compositionand/or reactor venting greatly decreases the cooling ability andtherefore greatly decreases the production rate.

Polyolefin Products

This disclosure also relates to compositions of matter produced by themethods described.

In some embodiments, the methods described produce ethylene homopolymersor ethylene copolymers, such as ethylene-α-olefin (e.g. C3 to C20)copolymers (such as ethylene-butene copolymers, ethylene-hexene and/orethylene-octene copolymers) having: a M_(w)/M_(n) of greater than 1 to4, or greater than 1 to 3.

Likewise, the processes of this disclosure produce ethylene copolymers.In some embodiments, the polyolefin copolymers produced have from about0 mol % to about 25 mol %, from about 0.5 mol % to about 20 mol %, fromabout 1 mol % to about 15 mol %, or from about 3 mol % to about 10 mol %of one or more C₃ to C₂₀ olefin comonomer. The one or more C₃ to C₂₀olefin comonomer may include C₃ to C₁₂ alpha-olefin, such as propylene,butene, hexene, octene, decene, or dodecene.

In some embodiments, the monomer is ethylene and the comonomer ishexene, for example, from about 1 mol % to about 15 mol % hexene, suchas about 1 mol % to about 10 mol %.

In at least one embodiment, the ethylene polymer composition is producedhaving: i) at least 50 mol % ethylene; ii) a density of 0.89 g/cc ormore, such as 0.918 g/cc or more, or 0.935 g/cc or more; and a g′vis ofabout 0.97 or greater.

In some embodiments, the polymers produced have an M_(w) of 5,000 g/molto 1,000,000 g/mol, such as 25,000 g/mol to 750,000 g/mol, or 50,000 to500,000 g/mol, and/or an M_(w)/M_(n), of greater than 1 to about 40,such as about 1.2 to about 20, about 1.3 to about 10, about 1.4 to about5, about 1.5 to about 4, or about 1.5 to about 3.

In at least one embodiment, the polymer produced has a unimodal ormultimodal molecular weight distribution as determined by Gel PermeationChromatography (GPC). By “unimodal” is meant that the GPC trace has onepeak or inflection point. By “multimodal” is meant that the GPC tracehas at least two peaks or inflection points. An inflection point is thatpoint where the second derivative of the curve changes in from negativeto positive or vice versa.

In at least one embodiment, the polymer produced has a bimodal molecularweight distribution as determined by Gel Permeation Chromatography(GPC). By “bimodal” is meant that the GPC trace has two peaks orinflection points.

Unless otherwise indicated modality, M_(w), M_(n), M_(z), MWD, g valueand g′_(vis) are determined by using a High Temperature Size ExclusionChromatograph (either from Waters Corporation or Polymer Laboratories),which may be equipped with a differential refractive index detector(DRI), a light scattering (LS) detector, and a viscometer. Experimentaldetails, including detector calibration, are described in: T. Sun, P.Brant, R. R. Chance, and W. W. Graessley, Macromolecules, Volume 34,Number 19, 6812-6820, (2001). The various transfer lines, columns anddifferential refractometer (the DRI detector) are contained in an ovenmaintained at 145° C. Solvent for the experiment is prepared bydissolving 6 grams of butylated hydroxytoluene as an antioxidant in 4liters of Aldrich reagent grade 1, 2, 4 trichlorobenzene (TCB). The TCBmixture is then filtered through a 0.7 μm glass pre-filter andsubsequently through a 0.1 μm Teflon filter. The TCB is then degassedwith an online degasser before entering the Size ExclusionChromatograph. Polymer solutions are prepared by placing dry polymer ina glass container, adding the desired amount of TCB, then heating themixture at 160° C. with continuous agitation for about 2 hours. Allquantities are measured gravimetrically. The TCB densities used toexpress the polymer concentration in mass/volume units are 1.463 g/ml atroom temperature and 1.324 g/ml at 145° C. The injection concentrationis from 0.75 to 2.0 mg/ml, with lower concentrations being used forhigher molecular weight samples. Prior to running each sample the DRIdetector and the injector are purged. Flow rate in the apparatus is thenincreased to 0.5 ml/minute, and the DRI is allowed to stabilize for 8 to9 hours before injecting the first sample. The LS laser is turned on 1to 1.5 hours before running the samples. The concentration, c, at eachpoint in the chromatogram is calculated from the baseline-subtracted DRIsignal, I_(DRI), using equation (E-15):

c=K _(DRI) I _(DRI)/(dn/dc)  (E-15)

where K_(DRI) is a constant determined by calibrating the DRI, and(dn/dc) is the refractive index increment for the system. For, therefractive index, n=1.500 for TCB at 145° C. and λ=690 nm. For purposesof this disclosure (dn/dc)=0.104 for propylene polymers, 0.098 forbutene polymers and 0.1 otherwise. Units on parameters throughout thisdescription of the SEC method are such that concentration is expressedin g/cm³, molecular weight is expressed in g/mole, and intrinsicviscosity is expressed in dL/g.

The LS detector is a Wyatt Technology High Temperature mini-DAWN. Themolecular weight, M, at each point in the chromatogram is determined byanalyzing the LS output using the Zimm model for static light scatteringof equation (E-16) (M. B. Huglin, LIGHT SCATTERING FROM POLYMERSOLUTIONS, Academic Press, 1971):

$\begin{matrix}{\frac{K_{o}c}{\Delta\;{R(\theta)}} = {\frac{1}{{MP}(\theta)} + {2A_{2}c}}} & \left( {E\text{-}16} \right)\end{matrix}$

where, ΔR(θ) is the measured excess Rayleigh scattering intensity atscattering angle θ, c is the polymer concentration determined from theDRI analysis, A₂ is the second virial coefficient [for purposes of thisdisclosure, A₂=0.0006 for propylene polymers, 0.0015 for butene polymersand 0.001 otherwise], (dn/dc)=0.104 for propylene polymers, 0.098 forbutene polymers and 0.1 otherwise, P(0) is the form factor for amonodisperse random coil, and K_(o) is the optical constant for thesystem in equation (E-17):

$\begin{matrix}{K_{o} = \frac{4\pi^{2}{n^{2}\left( {{dn}/{dc}} \right)}^{2}}{\lambda^{4}N_{A}}} & \left( {E\text{-}17} \right)\end{matrix}$

where N_(A) is Avogadro's number, and (dn/dc) is the refractive indexincrement for the system. For the refractive index, n=1.500 for TCB at145° C. and λ=690 nm.

A high temperature Viscotek Corporation viscometer, which has fourcapillaries arranged in a Wheatstone bridge configuration with twopressure transducers, is used to determine specific viscosity. Onetransducer measures the total pressure drop across the detector, and theother, positioned between the two sides of the bridge, measures adifferential pressure. The specific viscosity, η_(s), for the solutionflowing through the viscometer is calculated from their outputs. Theintrinsic viscosity, at each point in the chromatogram is calculatedfrom equation (E-18):

η_(s) =c[η]+0.3(c[η])²  (E-18)

where c is concentration and was determined from the DRI output.

The branching index (g′_(vis)) is calculated using the output of theabove SEC-DRI-LS-VIS method as follows. The average intrinsic viscosity,[η]_(avg), of the sample is calculated by equation (E-19):

$\begin{matrix}{\lbrack\eta\rbrack_{avg} = \frac{\sum{c_{i}\lbrack\eta\rbrack}_{i}}{\sum c_{i}}} & \left( {E\text{-}19} \right)\end{matrix}$

where the summations are over the chromatographic slices, i, between theintegration limits. The branching index g′_(vis) is defined usingequation (E-20):

$\begin{matrix}{{g^{\prime}{vis}} = \frac{\lbrack\eta\rbrack_{avg}}{{kM}_{v}^{\alpha}}} & \left( {E\text{-}20} \right)\end{matrix}$

where, for purpose of this disclosure, α=0.695 and k=0.000579 for linearethylene polymers, α=0.705 k=0.000262 for linear propylene polymers, andα=0.695 and k=0.000181 for linear butene polymers. M_(v) is theviscosity-average molecular weight based on molecular weights determinedby LS analysis.

In at least one embodiment, the polymer produced has a compositiondistribution breadth index (CDBI) of 50% or more, such as 60% or more,or 70% or more. CDBI is a measure of the composition distribution ofmonomer within the polymer chains and is measured by the proceduredescribed in PCT publication WO 93/03093, published Feb. 18, 1993,specifically columns 7 and 8 as well as in Wild et al, J. Poly. Sci.,Poly. Phys. Ed., Vol. 20, p. 441 (1982) and U.S. Pat. No. 5,008,204,including that fractions having a weight average molecular weight(M_(w)) below 15,000 are ignored when determining CDBI.

In another embodiment, the polymer produced has two peaks in the TREFmeasurement (see below). Two peaks in the TREF measurement as used inthis specification and the appended claims means the presence of twodistinct normalized ELS (evaporation mass light scattering) responsepeaks in a graph of normalized ELS response (vertical or y axis) versuselution temperature (horizontal or x axis with temperature increasingfrom left to right) using the TREF method below. A “peak” in thiscontext means where the general slope of the graph changes from positiveto negative with increasing temperature. Between the two peaks is alocal minimum in which the general slope of the graph changes fromnegative to positive with increasing temperature. “General trend” of thegraph is intended to exclude the multiple local minimums and maximumsthat can occur in intervals of 2° C. or less. In some embodiments, thetwo distinct peaks are at least 3° C. apart, at least 4° C. apart, or atleast 5° C. apart. Additionally, both of the distinct peaks occur at atemperature on the graph above 20° C. and below 120° C. where theelution temperature is run to 0° C. or lower. This limitation avoidsconfusion with the apparent peak on the graph at low temperature causedby material that remains soluble at the lowest elution temperature. Twopeaks on such a graph indicates a bimodal composition distribution (CD).An alternate method for TREF measurement can be used if the method belowdoes not show two peaks, i.e., see B. Monrabal, “CrystallizationAnalysis Fractionation: A New Technique for the Analysis of BranchingDistribution in Polyolefins,” Journal of Applied Polymer Science, Vol.52, 491-499 (1994).

TREF Method

Temperature Rising Elution Fractionation (TREF) analysis is done using aCRYSTAF-TREF 200+ instrument from Polymer Char, S.A., Valencia, Spain.The principles of TREF analysis and a general description of theparticular apparatus to be used are given in the article Monrabal, B.;del Hierro, P. Anal. Bioanal. Chem. 2011, 399, 1557. FIG. 3 of thearticle is an appropriate schematic of the particular apparatus to beused; however, the connections to the 6-port valve may differ from theapparatus to be used in that the tubing connected to the 11-o'clock portis connected to the 9-o'clock port and the tubing connected to the9-o'clock port is connected to the 11-o'clock port. Pertinent details ofthe analysis method and features of the apparatus to be used are asfollows.

1,2-Dichlorobenzene (ODCB) solvent stabilized with approximately 380 ppmof 2,6-bis(1,1-dimethylethyl)-4-methylphenol (butylated hydroxytoluene)is used for preparing the sample solution and for elution. The sample tobe analyzed (approximately 25 mg but as low as approximately 10 mg) isdissolved in ODCB (25 ml metered at ambient temperature) by stirring at150° C. for 60 min. A small volume (0.5 ml) of the solution isintroduced into a column (15-cm long by ⅜″ o.d.) packed with an inertsupport (of stainless steel balls) at 150° C., and the columntemperature is stabilized at 140° C. for 45 min. The sample volume isthen allowed to crystallize in the column by reducing the temperature to30° C. at a cooling rate of 1° C./min. The column is kept at 30° C. for15 min before injecting the ODCB flow (1 ml/min) into the column for 10min to elute and measure the polymer that did not crystallize (solublefraction). The infrared detector used (Polymer Char IR4) generates anabsorbance signal that is proportional to the concentration of polymerin the eluting flow. A complete TREF curve is then generated byincreasing the temperature of the column from 30 to 140° C. at a rate of2° C./min while maintaining the ODCB flow at 1 ml/min to elute andmeasure the dissolving polymer.

In at least one embodiment, the polymer produced has an ethylene contentof about 70 wt % or more, about 80 wt % or more, about 90 wt % or moreand/or a density of about 0.910 or more, such as about 0.93 g/cc ormore, about 0.935 g/cc or more, or about 0.938 g/cc or more. In someembodiments, the polymer produced has a density of 0.910 g/cc or more,alternately from 0.935 to 0.960 g/cc.

Examples

FIG. 5 is a graph illustrating an example linear regression used tocalculate a single equivalence factor in production of polyethylene witha density of 0.918 g/cm³ and an MI_(2.16) of 2 g/10 min. The sticklimits for iC5 and iC4 were plotted on a chart where the y-axis isstickiness temperature and the x-axis is partial pressure of the CA. Thelinear regression of the points for each individual CA provided a lineand the ratio of the slopes of those lines provided an equivalencefactor for one set of reactor conditions. The data of FIG. 5 demonstratethat, under these reactor conditions, an equivalence factor for iC4 is3.1 relative to iC5 by comparing the ratio of the slopes. The data inFIG. 5 were obtained by the laboratory method described in in U.S. Pat.No. 10,029,226.

Table 2 (in parts 2.1 and 2.2) shows an example equivalence factorlinear regression table of coefficients:

TABLE 2.1 Intercept Temperature Pressure MI Density C2= iC4  7.489−7.55E−03  4.38E−04 2.24E−03 −3.186  −0.404  nC4  6.623 −2.88E−03 9.84E−05 2.39E−03 −4.325  −0.175  C4=  10.102 −4.13E−03  1.92E−044.03E−03 −7.691  −0.218  nC5  1.128 1.86E−04 5.88E−05 2.38E−04 −0.400 0.004 nC6  −0.254 5.90E−04 6.59E−05 −2.45E−04  0.501 0.024 C6=  0.0835.79E−04 7.45E−05 −7.67E−05  0.133 0.024 Cis-2 C6=  −0.122 7.46E−045.14E−05 −1.57E−04  0.332 0.021 Trans-2 C6=  −0.231 8.27E−04 4.15E−05−2.18E−04  0.459 0.021

TABLE 2.2 nC4 iC4 C4= nC5 iC5 nC6 C6= iC4  −0.729 n/a 0.279 0.268  1.354.039  3.283 nC4 n/a −0.281  0.133 0.119  0.819 1.373  0.882 C4= −0.22−0.284  n/a 0.551  1.175 2.637  2.21 nC5  0.006 0.019 0.098 n/a  0.278−0.217   −0.278 nC6  0.042 0.054 0.095 −0.022   0.127 n/a  −0.267 C6= 0.069 0.068 0.066 0.066  0.19 −0.031  n/a Cis-2 C6=  0.033 0.046 0.099−0.039   0.115 −0.257  −0.34 Trans-2 C6=  0.022 0.039 0.111 −0.068  0.099 −0.328   −0.424

The combination of factors in the linear regression led to an equationto allowing calculation of the equivalence factor for relating iC4 toiC5 of:

αiC4=7.489−0.00755T+0.000438P+0.00224MI−3.186ρ−0.404X _(C2=)−0.729X_(nC4)+0.279X _(C4=)+0.268X _(nC5)+1.350X _(iC5)+4.039X _(nC6)+3.283X_(C6=).

Where T=Reactor Temperature (° F.); P=Reactor Pressure (psia); MI=ResinMelt Index (g/10 min); ρ=Resin Density (g/cc); X_(C2=)=Mole Fraction ofEthylene in the Reactor Cycle Gas; X_(nC4)=Mole Fraction of n-Butane inthe Reactor Cycle Gas; X_(C4=)=Mole Fraction of 1-Butene in the ReactorCycle Gas; X_(nC5)=Mole Fraction of n-Pentane in the Reactor Cycle Gas;X_(iC5)=Mole Fraction of Isopentane in the Reactor Cycle Gas;X_(nC6)=Mole Fraction of n-Hexane in the Reactor Cycle Gas; andX_(C6=)=Mole Fraction of 1-Hexene in the Reactor Cycle Gas. In thisexample, the regression equation for the equivalence factors wasdeveloped by using the thermodynamic estimates from the method describedabove (in paragraphs [0135-0145]). The various variables in the linearregression were adjusted over wide ranges to allow the development ofthe described regression equation. The regression equation is suitableunder the ranges of reactor conditions used to develop the model, butfurther extrapolation could result in inaccuracies.

FIG. 6 is a graph of mole percentages of condensing agent over time withreactor conditions under DCS control and reactor conditions with manualcontrol. Where a controlling system is used to calculate the correctratio of CAs and automatically adjust as the reactor conditions change,the amounts of CAs can be increased, cooling improved, and thereforeproduction rates increased.

FIG. 7 is a graph of total condensing agent composition versus predictedproduction rate. As the total CA composition is increased, the overallproduction rate is increased. Line 701 shows an equivalence factor foriC5 and iC4 of 3.1, a total SL_(iC5) of 16.5 mol %, with 1.0 mol % C6inerts (static). Line 703 shows an equivalence factor for iC5 and iC4 of2.4, a total SL_(iC5) of 17 mol %, with 0.8 mol % C6 inerts (static).Line 705 shows an equivalence factor for iC5 and iC4 of 2.4, a totalSL_(iC5) of 16 mol %, with 1.0 mol % C6 inerts (static). Line 707 showsan equivalence factor for iC5 and iC4 of 2.4, a total SL_(iC5) of 14.5mol %, with 1.5 mol % C6 inerts (static). The total allowable CA (Z) isthe x-axis and the y-axis is the predicted production rate.

FIG. 8 is a graph illustrating data generated from commercial processengineering simulation software showing amount of iC4 replacing removediC5 versus production rate relative to running a gas phasepolymerization with only iC5 for an LLDPE having a density of 0.918 g/ccand an MI_(2.16) of 1 g/10 min. PROII is a software package that allowsfor steady state simulation of process engineering. A polymerizationsystem was modelled, and the production rate calculated for varying CAcompositions, as iC4 was increased and iC5 decreased with an equivalencefactor of 3.1. The plot of the simulated data gave a maximum productionat approximately 12.4 mol % of iC4. The reaction conditions were set sothat the reactor had a total allowable CA composition of 25.4%, thestick limit of iC5 was 17% and the equivalence factor was 3.1. Usingequation E-14, it was found that 4 mol % of the iC5 may be replaced by4×3.1 or 12.4 mol % of iC4, where the same maximum was obtained in asimple calculation rather than a simulation of 7 different iC4 amounts.For this simulation PRO/II software produced by SimSci™ was used.

FIG. 9 is a graph illustrating data generated from commercial processengineering simulation software showing amount of nC4 replacing removediC5 versus production rate relative to running a gas phasepolymerization with only iC5 for an LLDPE having a density of 0.918 g/ccand an MI_(2.16) of 1 g/10 min. A polymerization system was modelled andthe production rate calculated for varying CA compositions, as nC4 wasincreased and iC5 decreased with an equivalence factor of 2. The plot ofthe simulated data gave a maximum production at approximately 16.8 mol %of nC4. The reaction conditions were set so that the reactor had a totalallowable CA composition of 25.4%, the stick limit of iC5 was 17% andthe equivalence factor was 2. Using formula F-1, it was found that that8.4 mol % of the iC5 may be replaced by 8.4×2 or 12.4 mol % of nC4, thesame maximum was obtained in a simple calculation rather than asimulation of 9 different iC4 amounts. For this simulation PRO/IIsoftware produced by SimSci™ was used.

FIG. 10 is a graph comparing production rate as a second CA replaces atleast a portion of iC5 according to an equivalence factor relating thesecond CA with iC5 in a CA composition using a Z of 25 mol % and anSL_(CA1) of 15 mol %. The secondary CAs were iC4 and nC4 with iC4providing a greater overall production rate at approximately 85tonnes/hour, where the nC4 composition had a maximum production rateabove 83 tonnes/hour. In order to determine if a three component mixtureprovided added benefit, a ternary CA composition was tested where nC4was increased in the iC5/iC4 mixture that provided production ofapproximately 85 tonnes/hour. The addition of nC4 to this mixtureprovided no additional benefit. As nC4 was increased, the productionrate decreased.

Because binary CA compositions may provide the greatest production rateimprovement, the balance of CAs within a CA composition providesvaluable cost benefit in the production of polyolefins in the gas phase.

FIG. 11 is a graph illustrating production rate as a second CA replacesat least a portion of iC5 according to an equivalence factor relatingthe second CA with iC5 in a CA composition using a Z of 25 mol % and anSL_(CA1) of 15 mol %. The secondary CAs were iC4 and C3 with iC4providing a greater overall production rate at approximately 85tonnes/hour, where the C3 composition had a maximum production rate ofabout 77 tonnes/hour. In order to determine if a three component mixtureprovided added benefit, a ternary CA composition was tested where theamount of iC4 was increased in the iC5/C3 mixture that providedproduction of greater than 77 tonnes/hour. The addition of iC4 to thismixture improved the production rate, but not greater than theproduction rate of the CA composition containing only iC4 and iC5.

FIG. 12 is a graph illustrating production rate as a second CA replacesat least a portion of iC5 according to an equivalence factor relatingthe second CA with iC5 in a CA composition using a Z of 25 mol % and anSL_(CA1) of 15 mol %. The secondary CAs were iC4 and neoC5 with neoC5providing a greater overall production rate at approximately 87tonnes/hour, where the iC4 composition had a maximum production rate ofapproximately 85 tonnes/hour. In order to determine if a three componentmixture provided added benefit, a ternary CA composition was testedwhere the amount of neoC5 was increased in the iC5/iC4 mixture. Becausethe stick limit was reached before the total allowable CA compositionwas reached in the binary neoC5/iC5 mixture, the ternary CA compositionis shown to have greater production rates than the neoC5/iC5 peak. Ifthe stick limit had not been reached before the total allowable CAcomposition, the binary CA composition would have had the greaterproduction consistent with the results shown in FIGS. 10 and 11.

FIG. 13 is a graph illustrating the polymer production rates of examplebinary CA compositions as a second CA replaces at least a portion of iC5according to an equivalence factor relating the second CA with iC5.Under the reaction conditions of these tests, the neoC5 provided thegreatest production rate improvement, but reached the stick limit beforeits inflection point. iC4 provided the next best production rateimprovement. The binary CA compositions tested do not include allpossible binary CA compositions, but include many typically used andevaluated compositions.

FIG. 14 is a graph illustrating polymer production rate versus total CAfor example binary CA compositions, where neoC5 is intentionallyexcluded because of lower availability. FIG. 14 demonstrates that whereSL_(iC5) is 10 mol % certain binary CA compositions provide improvedproduction in certain ranges of total allowable CA. For example, if thetotal allowable CA is about 10 mol % or less, a CA composition includingnC6 and iC5 can provide improved production. If the total allowable CAis from about 10 mol % to about 30 mol %, a CA composition including iC5and iC4 can provide improved production. Lastly, if the total allowableCA is about 30 mol % or greater, a CA composition including iC4 and C3can provide improved production. Without being limited by theory, thegeneral trend observed is that beyond the stick limit of the morevolatile component, a new binary CA composition provides improvedproduction. If total allowable CA composition is greater than the sticklimit of the more volatile component, improved rates may be achieved byusing more volatile CA components, for example using the more volatileCA component of the binary CA composition from the previous stickinessregion, combined with an even more volatile CA component. For example,since the stick limit of neoC5 in the neoC5/iC5 binary mixture wasreached before the total allowable CA in FIG. 12, an improved productionrate would be observed for a binary neoC5/iC4 mixture, even greater thanthe ternary neoC5/iC4/iC5 mixture. In this example, neoC5 would be themore volatile CA component from the previous stickiness region, and iC4would be the more volatile component added. FIGS. 14 and 15 illustratecertain advantages of example binary CA compositions over othercompositions.

FIG. 15 is a graph illustrating polymer production rate versus total CAfor binary CA compositions, where neoC5 is included. As shown in FIG.15, additional total CA composition may provide additional regions wherethe production is improved by changing the binary CA composition.Furthermore, where SL_(iC5) is 10 mol %, certain binary CA compositionsprovide improved production in certain ranges of total allowable CA. Forexample, if the total allowable CA is about 10 mol % or less, a CAcomposition including nC6 and iC5 can provide improved production. Wherethe total allowable CA is from about 10 mol % to about 17 mol %, a CAcomposition including iC5 and neoC5 can provide improved production.Where the total allowable CA is from about 17 mol % to about 30 mol %, aCA composition including neoC5 and iC4 can provide improved production.Lastly, if the total allowable CA is about 30 mol % or greater, a CAcomposition including iC4 and C3 can provide improved production.

The regions in which a CA composition provides maximum production werecalculated based on static equivalence factors. The boundaries of aparticular region may be calculated by multiplying the stick limit ofthe first condensing agent by the equivalence factor of the secondcondensing agent in the binary CA composition providing the improvedproduction rate. The CA composition providing improved production for aspecific set of reactor conditions may change as reactor conditionschange including production of varying grades of polyolefin allowing fordifferent total allowable CA. The stickiness region boundaries can becalculated by multiplying the SL_(CA1) term by the equivalence factor ofthe more volatile component in the combination of CAs with the greatestproduction rate.

FIGS. 10-15 demonstrate that, under these conditions, a CA compositioncontaining two CAs is more effective than the corresponding ternary CAcompositions. Without being limited by theory, the binary CAcompositions with the greatest production rate improvements arenegatively affected by the addition of additional CAs, and provideimproved production under certain reactor conditions over CAcompositions containing three or more CAs.

FIG. 16 is a plot of an operability window for avoiding agglomeration ofresins. As shown in the plot, the temperature of the reactor and theequivalent partial pressure of the first CA define a two dimensionalspace for reactor operations. In the plot, the x-axis represents theequivalent partial pressure of the first CA, iC5 in this example. They-axis represents the reactor temperature. The predicted upperstickiness temperature is plotted as the upper dashed line 1602. At aspecific temperature, the concentration of a first CA that crosses line1602 is the stick limit, as passing that point causes stickiness.Because sticking in the reactor may cause reactor shutdown, anartificial upper limit may be placed to reduce or eliminate risk ofagglomeration, represented by line 1604. This artificial upper limitprovides a buffer for error in the measured or calculated upperstickiness temperature. The artificial upper limit is shown as 10° C.,but such a large buffer is not required, especially if the CAcomposition is automatically controlled. The lower stickinesstemperature (the gas phase composition dew point) is plotted as lowerdashed line 1606, and, similar to the upper stickiness temperature, mayhave an artificial lower limit 1608 placed as a buffer for error toavoid potential issues with sticking or agglomeration (the dew pointlimit). At a specific CA concentration, the temperature that crossesline 1606 is the dew point limit, as passing that point causescondensation and stickiness. The artificial lower limit may account forcapillary condensation which may take place at a temperature higher thanthe dew point. The artificial lower limit is shown as 10° C., but such alarge buffer is not required, especially if the CA composition isautomatically controlled and reactor fluidization is monitored.

The artificial upper limit 1604 and the artificial lower limit 1608define a non-sticking regime 1610 for the reactor. Other areas definedby these limits are sticking regimes, where the combination oftemperature or condensation of the gas phase composition combine to makethe resin sticky. In area 1612, the higher temperature increases thesolubility of the gas phase composition in the polymer resin causingstickiness. In area 1614, the high temperature and high equivalentpartial pressure of the first CA combines to create a sticking regime inwhich a portion of the gas phase composition condenses to a liquid andthe temperature increases the solubility of the gas and liquid in thepolymer resin. Sticking regime 1616 is a liquid regime in which the gasphase composition begins to condense and make the resin sticky. Square1618 represents a set of reactor conditions operating withinnon-sticking regime 1610. An operator, or control system can alterreactor conditions to move square 1618 towards the point at which thelimits 1604 and 1608 meet in order to increase productivity, whilestaying within the confines of non-sticking regime 1610. As reactorconditions are moved toward the point at which the limits 1604 and 1608meet, operations become less flexible and the room for error reduces,making process upsets, including temperature, pressure, andconcentration deviations, more problematic.

FIG. 17 is a graph illustrating production rates for production of apolyethylene polymer with a density of 0.918 g/cm³ and an MI_(2.16) of1.0 g/10 min with a reactor pressure of 320 psig. The production ratesare related to the total allowable CA composition at varying equivalencefactors relating iC5 and iC4. Production rates increase in a near linearfashion in relation to the total allowable CA composition and correlateto the equivalence factor used. Line 1702 represents an iC4/iC5equivalence factor of 3, line 1704 represents an iC4/iC5 equivalencefactor of 2.75, and line 1706 represents an iC4/iC5 equivalence factorof 2.46.

FIG. 18 is a graph illustrating gas phase composition dew point inproduction of a polyethylene polymer with a density of 0.918 g/cm³ andan MI_(2.16) of 1.0 g/10 min with a reactor pressure of 320 psig. Thegas phase composition dew point is graphed against to the totalallowable CA composition at varying equivalence factors relating iC5 andiC4. Line 1802 represents an iC4/iC5 equivalence factor of 3, and theupward slop of the line demonstrates an increase in gas phasecomposition dew point as total allowable CA composition is increased.Line 1804 represents an iC4/iC5 equivalence factor of 2.75, and the nearflat slope of Line 1804 demonstrates that a change in the equivalencefactor may maintain gas phase composition dew point over a range oftotal allowable CA composition. Furthermore, Line 1806 represents aniC4/iC5 equivalence factor of 2.46, and the downward slope of Line 1806demonstrates a decrease in gas phase composition dew point as totalallowable CA composition is increased. In combination, the various linesdemonstrate that the change in equivalence factor may have a significanteffect on dew point within the reactor. A comparison of FIG. 17 and FIG.18 demonstrates that decreasing the equivalence factor may have a largeeffect on the dew point of the gas phase composition in the reactorwhile not greatly affecting the production rate.

FIG. 19 is a graph illustrating the stick limit and the dew point limitas a function of production rate and total allowable CA composition.Line 1902 represents the stick limit, and line 1904 represents the dewpoint limit. Point 1906 represents a theoretical failure past the dewpoint limit that can be corrected by either reducing the total allowableCA composition or reducing the equivalence factor relating the CAswithin the CA composition. Point 1908 is the point at which the sticklimit and the dew point limit intersect and point 1910 represents achange in the equivalence factor of 0.1. It can be ascertained thatreduction of the total allowable CA composition along the stick limit(represented by arrow 1912) causes a greater loss in production ratethan reduction of the equivalence factor until conditions do not passthe dew point limit (represented by arrow 1914). Increasing theequivalence factor may yield an increase in production rate.Additionally, the incremental impact on production rate is lower forchanges in equivalence factor than for changes made to total allowableCA composition.

Overall, it has been found that the ratios of CAs in a CA compositionmay be calculated using simplification of the many factors that affectstickiness, including solubility and dew point of the gas phasecomposition within a reactor in the production of polyolefin. Thecalculation allows for adjustments to the ratio of the CAs in a CAcomposition to take place in real time and allows for control of theadjustments by a control system processing reactor conditions andadjusting the CA composition accordingly. The calculation of, andadjustments made to, the CA composition may allow for increasedproduction rates of polyolefin relative to previous processes. Forexample, in regards to nearing the dew point of a gas phase compositionin a reactor, previous processes included decreasing total allowable CAcomposition causing a significant loss in production rate.

While the present disclosure has been described with respect to a numberof embodiments and examples, those skilled in the art, having benefit ofthis disclosure, will appreciate that other embodiments can be devisedwhich do not depart from the scope and spirit of the present disclosure.

What is claimed is:
 1. A method to polymerize olefins with control ofcondensed phase cooling in a gas phase reactor, the method including:introducing one or more polymerization catalysts and one or more olefinmonomers in a gas phase polymerization reactor; introducing a condensingagent composition comprising a first condensing agent and a secondcondensing agent in a ratio of first condensing agent to secondcondensing agent, wherein the ratio of the first condensing agent to thesecond condensing agent is calculated by: ascertaining a stick limit fora first condensing agent, calculating an equivalence factor relating thefirst condensing agent and a second condensing agent, ascertaining atotal allowable condensing agent, and calculating a first amount of thefirst condensing agent removed and replaced by a second amount of thesecond condensing agent calculating the dew point limit of a gas phasecomposition comprising the one or more olefin monomers, the firstcondensing agent, and the second condensing agent, producing acalculated dew point limit; determining if introducing a mixturecomprising the one or more olefin monomers and the condensing agentcomposition would fall below the calculated dew point limit; withdrawinga polyolefin product; withdrawing a gas phase composition comprising atleast a portion of the first condensing agent and the second condensingagent; condensing a portion of the gas phase composition yielding acondensed stream; and recycling at least a portion of the condensedstream to the gas phase reactor.
 2. The method of claim 1, whereincalculating a first amount of the first condensing agent removed andreplaced by a second amount of the second condensing agent isaccomplished using equation (E-14): $\begin{matrix}{X = \frac{Z - {SL}_{{CA}\; 1}}{{\alpha\;{CA}\; 2} - 1}} & \left( {E\text{-}14} \right)\end{matrix}$ wherein X is the first amount of the first condensingagent removed and replaced by the second amount of the second condensingagent, where the second amount is X multiplied by αCA2, Z is the totalallowable condensing agent, SL_(CA1) is the stick limit for the firstcondensing agent, and αCA2 is the equivalence factor relating the firstcondensing agent and the second condensing agent.
 3. The method of claim1, wherein if introducing the mixture comprising the one or more olefinmonomers and the condensing agent composition exceeds the calculated dewpoint limit, then the equivalence factor is reduced incrementally untilintroducing the mixture comprising the one or more olefin monomers andthe condensing agent composition does not exceed the calculated dewpoint.
 4. The method of claim 1, wherein if introducing the mixturecomprising the one or more olefin monomers and the condensing agentcomposition exceeds the calculated dew point limit, then the stick limitfor a first condensing agent is reduced incrementally until introducingthe mixture comprising the one or more olefin monomers and thecondensing agent composition does not exceed the calculated dew point.5. The method of claim 1, wherein the total allowable condensing agentcomposition is increased by either increasing reactor pressure or bydecreasing partial pressure of nitrogen in the reactor.
 6. (canceled) 7.The method of claim 1, wherein the first condensing agent and the secondcondensing agent are independently selected from C3-C6 hydrocarbons. 8.The method of claim 1, wherein the one or more olefin monomers comprisesethylene.
 9. The method of claim 1, wherein the one or more olefinmonomers comprises ethylene and a comonomer selected from propylene,1-butene, 1-hexene, or 1-octene.
 10. The method of claim 1, wherein thepolyolefin product has a density of about 0.890 g/cm³ to about 0.930g/cm³ and a g′vis of about 0.97 or greater.
 11. The method of claim 1,wherein the first condensing agent and the second condensing agent areone of the following pairs: (a) the first condensing agent is isopentaneand the second condensing agent is isobutane; (b) the first condensingagent is isobutane and the second condensing agent is n-butane; (c) thefirst condensing agent is n-hexane and the second condensing agent isiso-pentane; (d) the first condensing agent is isobutane and the secondcondensing agent is propane; (e) the first condensing agent isisopentane and the second condensing agent is neo-pentane; the firstcondensing agent is neo-pentane and the second condensing agent isisobutane. 12.-16. (canceled)
 17. The method of claim 1, whereindetermining the stick limit is performed using a thermodynamicestimation of hydrocarbon solubility.
 18. The method of claim 1, whereindetermining the stick limit is performed by a laboratory stickinesstemperature test.
 19. The method of claim 1, wherein determining theequivalence relating the first condensing agent and the secondcondensing agent is performed using thermodynamic estimation as afunction of pressure, temperature, melt index, gas composition, anddensity.
 20. The method of claim 1, wherein determining the equivalencerelating the first condensing agent and the second condensing agent isperformed by calculating the ratio of stickiness temperature versuspartial pressure slopes of the first condensing agent and the secondcondensing agent.
 21. The method of claim 1, wherein determining theequivalence factor relating the first condensing agent and the secondcondensing agent is performed by entering data into an equation relatingthe equivalence factor to reactor conditions.
 22. The method of claim 1,further comprising adjusting the ratio of first condensing agent tosecond condensing agent as reactor conditions change with a controlsystem.
 23. The method of claim 22, wherein the control system comprisesa DCS control.
 24. The method of claim 1, wherein the condensing agentcomposition is substantially free of C3 to C6 hydrocarbons other thanthe first condensing agent and the second condensing agent.
 25. Themethod of claim 1, wherein the gas phase composition is substantiallyfree of C3 to C6 aliphatic hydrocarbons other than the first condensingagent, the second condensing agent.
 26. The method of claim 1, whereinthe recycling the at least a portion of the condensed stream to the gasphase reactor further comprises adding one or more of the firstcondensing agent or the second condensing agent to the condensed stream.